<?xml version="1.0" encoding="UTF-8"?><rss xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:atom="http://www.w3.org/2005/Atom" version="2.0"><channel><title><![CDATA[RSS Feed]]></title><description><![CDATA[RSS Feed]]></description><link>http://direct.ecency.com</link><image><url>http://direct.ecency.com/logo512.png</url><title>RSS Feed</title><link>http://direct.ecency.com</link></image><generator>RSS for Node</generator><lastBuildDate>Tue, 21 Apr 2026 23:23:18 GMT</lastBuildDate><atom:link href="http://direct.ecency.com/created/geogebra/rss.xml" rel="self" type="application/rss+xml"/><item><title><![CDATA[Velocity and Acceleration as Derivatives of the Position Vector + Example of an Object moving in 2D]]></title><description><![CDATA[In this video, I show that the derivative of the position vector of a particle moving in 3D space is just the velocity, and likewise the acceleration is obtained as the derivative of the velocity. Thus,]]></description><link>http://direct.ecency.com/hive-111030/@mes/velocity-and-acceleration-as-derivatives-of-the-position-vector-example-of-an-object-moving-in-2-d</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/velocity-and-acceleration-as-derivatives-of-the-position-vector-example-of-an-object-moving-in-2-d</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 21 Apr 2026 16:25:51 GMT</pubDate><enclosure url="https://images.ecency.com/p/QVdSJhgNm7rytEdw6Y8ua3ELysg9umAYoQxsRewpowcr9BKTDetB9PLAyFNdumXwwoGQ6UnYtDm7pjA6VAC7SAt9KgUH9AqzcgnhCZxKgfJY8U6ctVPwcAihgMyeSB1kf6C1wW5kJG6wtxv9eNHLAPvvYxeqf7fQm3Q2KnmYF2biHYoqP7BM9wM?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Velocity and Acceleration as Derivatives of the Position Vector + Example of an Object moving in 2D]]></title><description><![CDATA[In this video, I show that the derivative of the position vector of a particle moving in 3D space is just the velocity, and likewise the acceleration is obtained as the derivative of the velocity. Thus,]]></description><link>http://direct.ecency.com/hive-128780/@mes/cf69f664</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/cf69f664</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 21 Apr 2026 04:35:09 GMT</pubDate><enclosure url="https://images.ecency.com/p/46aP2QbqUqBqwyMYx5rqy9vFZMnbeMhRu3KsA83BYsWYwubDhnkHxNwYeWhd3bKNx2tz5LvhbtF82ogFCJ8JiqHpneST?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[The TNB Frame: Normal and Osculating Planes + Example on a Circular Helix]]></title><description><![CDATA[In this video, I go over the TNB Frame for space curves and their associated Normal and Osculating Planes, which have applications in the motion of spacecraft. The TNB Frame is named after the Tangent,]]></description><link>http://direct.ecency.com/hive-128780/@mes/msfarvob</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/msfarvob</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 13 Jan 2026 22:05:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfKKVdjVdTJeZeR9mpZgJwQ4CSCx3drLVVDsK6aqan538K6ZgEQ2mYBEypXpEcuZiFeF5t7bb548582A?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Normal and Binormal Vectors + Example on a Circular Helix]]></title><description><![CDATA[In this video, I go over the principal unit normal and binormal vectors of a space curve, which are both derived from the unit tangent vector. YouTube - Summary - Notes - Playlist - Vector Functions playlist]]></description><link>http://direct.ecency.com/hive-111030/@mes/normal-and-binormal-vectors-example-on-a-circular-helix</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/normal-and-binormal-vectors-example-on-a-circular-helix</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Sun, 11 Jan 2026 22:43:09 GMT</pubDate><enclosure url="https://images.ecency.com/p/3ejZQFLqXedKXKhURdjx14Sr8NSYZmTdw2HQuQXkeUsn4X1LM6CBB673MURi3E19AyAMBuu9sLH3sbJZXcJhajNGM3FqgbcgyFL5KJoMybiwwwvsQWf99dF8APvGjVcSjee5paYSYpddt8Vq5ZAf5oux6CTdBtrTTTLN2p7fTQQwjHxtsue6WYxi5LA1M?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Arc Length of a Space Curve + Example on Circular Helix]]></title><description><![CDATA[In this video, I extend the formula for the arc length of a 2D plane curve to that of a 3D space curve, both of which can be represented in compact form as the integral of the length of the derivative]]></description><link>http://direct.ecency.com/hive-128780/@mes/nizhfvfl</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/nizhfvfl</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 26 Dec 2025 22:05:09 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfKKVdjVeDx4VBSZLpZVzA9Vk3cg3Vr3zjfr2EQd3VBBPFZZYsDDcGTyjYEDRtsH7GwGPybn78D82dZ8?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Vector Functions: Arc Length and Curvature]]></title><description><![CDATA[In this video, I go over further into vector functions and this time do a deep dive into the arc length and curvature of a space curve. The arc length for a space curve is calculated in much the same way]]></description><link>http://direct.ecency.com/hive-128780/@mes/koxharrd</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/koxharrd</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 23 Dec 2025 06:30:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/S5Eokt4BcQdk7EHeT1aYjzebg2hC7hkthT45eJK5tKNu6VKP6DmSGWe5KB35i9Ypd2R26JJ?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Example 4: Tangent Vector is Orthogonal to Vector of Constant Length]]></title><description><![CDATA[In this video I show that the tangent vector (derivative of a vector function) is orthogonal or perpendicular to a vector of constant length. Geometrically this means that the curve is on the surface of]]></description><link>http://direct.ecency.com/hive-147010/@mes/example-4-tangent-vector-is-orthogonal-to-vector-of-constant-length</link><guid isPermaLink="true">http://direct.ecency.com/hive-147010/@mes/example-4-tangent-vector-is-orthogonal-to-vector-of-constant-length</guid><category><![CDATA[hive-147010]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 08 Oct 2025 04:21:09 GMT</pubDate><enclosure url="https://images.ecency.com/p/2xVmzkbNCvpwrGAp45WKwgAaUaJnmHfvZ7RZqiyQWofSGyTTtrRkun2oTNhMujgHTbeh57HN8TbntLp7sN6jbBq5yEP9j3DMJq4YyhAsCF4683mW8cBzyZcY8Z38SPoCzUjR4ciaW7BLL6KxYnbivoNwLgnGDkpYgStkNkj9zM397mEu8cK5CEvyqnwJ3W7zBqCCf1No?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Example 3: Tangent Line to a Helix]]></title><description><![CDATA[In this video I show how to obtain the parametric equations of a line that is tangent to a given point on a helix, whose parametric equations are also given. YouTube - Summary - Notes - Playlist - Vector]]></description><link>http://direct.ecency.com/hive-111030/@mes/example-3-tangent-line-to-a-helix</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/example-3-tangent-line-to-a-helix</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 30 Sep 2025 22:26:24 GMT</pubDate><enclosure url="https://images.ecency.com/p/FUkUE5bzkAZSUQtscfU67XyuspKfVPvhJ6PgMwaumQRFSqc8YzUHX1PdV8Ecid6T9MzvyLPJfmLG7mYtzvg3RQvjgvJEbucz8HKJTcAykQoaBY4DyVNPuRKLw7vWfv3dzqG5QUgDgJjimD5faVTjWCbKwQqmTtJYhWDM?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Example 3: Tangent Line to a Helix]]></title><description><![CDATA[In this video I show how to obtain the parametric equations of a line that is tangent to a given point on a helix, whose parametric equations are also given. I first convert the helix parametric equations]]></description><link>http://direct.ecency.com/hive-128780/@mes/yfpyxeyr</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/yfpyxeyr</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Mon, 29 Sep 2025 17:10:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfHesJoVuQ1R8G8Xa1bWydzYUjVa7SAE7vaFhEWf8qYZzK6Ygh7Xp4co5JB7ZksEehyvQNcoosGYcrgn?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Example 2: Sketching the Tangent Vector]]></title><description><![CDATA[In this video I go over another example on derivatives of vector functions, and this time sketch the tangent vector to a plane curve manually as well as with GeoGebra's 3D graphing calculator. The tangent]]></description><link>http://direct.ecency.com/hive-128780/@mes/vrcvsdfe</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/vrcvsdfe</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Fri, 26 Sep 2025 21:05:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfHesJoVxX1mENP6R8LAQ2PYAZkzfxgcSg4ufpzBKHGgZc3abfSoprPGnHS3zyAwRbFenihUzjEqUvnr?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Definition of Derivative for Vector Functions]]></title><description><![CDATA[In this video I go over the definition of derivative for a vector function, which is very similar to the definition for real valued functions. The derivative of a vector function is defined as the limit]]></description><link>http://direct.ecency.com/hive-111030/@mes/definition-of-derivative-for-vector-functions</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/definition-of-derivative-for-vector-functions</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 17 Sep 2025 04:14:09 GMT</pubDate><enclosure url="https://images.ecency.com/p/2xVmzkbNCvpwrGAp45WKwgAaUaJnmHfvZ7RZqiyQWofSGyTTtrRkun2rS8GKML2yawzCu5frXpqKJMSHZ9qUhD4AZqFJqSXDMeXuEi4wbFfigi1pcVzLbxo9SvsVzRtMckrH6BndJQURmumgSKuieK2HaV157kV3JiJehHGSVUNxb8XugbiwbEj2zXQjrfu7HBG9VbT5?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Definition of Derivative for Vector Functions]]></title><description><![CDATA[In this video I go over the definition of derivative for a vector function, which is very similar to the definition for real valued functions. The derivative of a vector function is defined as the limit]]></description><link>http://direct.ecency.com/hive-128780/@mes/jfezftxf</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/jfezftxf</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 16 Sep 2025 04:44:09 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfHesJoVziURmfLRjrbk2Xzdc8q81Tn4vSpGABf5rvcRtJ4YzEMZmCu5JT8wdSBj45ftWnxmkUgAVp14?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Exercise 3: Manually Graphing the Projection of the Trefoil Knot onto the xy-Plane]]></title><description><![CDATA[In this video I manually (and painstakingly) plot an approximation of the projection of the 3D trefoil knot onto the xy-plane. I begin by converting the parametric equations of the trefoil knot into polar]]></description><link>http://direct.ecency.com/hive-128780/@mes/hkognzwv</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/hkognzwv</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 09 Jul 2025 01:52:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfKKVdjVcN11F7PD5nTnzwTv2oCn17Z8ZqB3bUVh3xfJfh29Eqby71TpVLnF1gcg9H1kq46pjoiyaGQN?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Charged Particles Moving in Electromagnetic Fields]]></title><description><![CDATA[In this video I show that space curves can be used to model charged particle motion in orthogonally oriented electric and magnetic fields. Depending on the speed and position of a charged particle, the]]></description><link>http://direct.ecency.com/hive-111030/@mes/charged-particles-moving-in-electromagnetic-fields</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/charged-particles-moving-in-electromagnetic-fields</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Wed, 25 Jun 2025 22:52:09 GMT</pubDate><enclosure url="https://images.ecency.com/p/LcTxR7u1XKaa3e4SzxK7yqWuV3S4XK8xR2EcsKHri52uLcFxE8Xmgc9JdvkHGVKUjQMKGYndP1H7sLWYWVdAVthJgHpsGjVGyDVMAxGjgfUgbBw2SVgcsA29R9FNnLY7sHCy6g9y5FcG3Zo1xvnwjXM91?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Example 7: Using Computers (GeoGebra) to Draw Space Curves]]></title><description><![CDATA[In this video I graph out several complicated space curves using GeoGebra's amazing 3D graphing calculator. These curves are the toroidal spiral, trefoil knot, and a twisted cubic. YouTube - Summary -]]></description><link>http://direct.ecency.com/hive-111030/@mes/example-7-using-computers-geo-gebra-to-draw-space-curves</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/example-7-using-computers-geo-gebra-to-draw-space-curves</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 24 Jun 2025 04:18:48 GMT</pubDate><enclosure url="https://images.ecency.com/p/7b4bio5hobgskW8qdJJeDjrJHTiT5uLGk5BQErotAHijnZQZsvzoyRYzi5289LX8EPneGyzratRSBqNSAuJqmTgAJKteAeinRVvdi2WRby4f8YQiCke41UvpVqFWcWZRxoGSFYsBJVhTsUXj3TKv2NGfnbYT?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Example 7: Using Computers (GeoGebra) to Draw Space Curves]]></title><description><![CDATA[In this video I graph out several complicated space curves using GeoGebra's amazing 3D graphing calculator. These curves are the toroidal spiral, trefoil knot, and a twisted cubic. I illustrate the importance]]></description><link>http://direct.ecency.com/hive-128780/@mes/ewfhgotg</link><guid isPermaLink="true">http://direct.ecency.com/hive-128780/@mes/ewfhgotg</guid><category><![CDATA[hive-128780]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 24 Jun 2025 03:31:06 GMT</pubDate><enclosure url="https://images.ecency.com/p/99pyU5Ga1kwr5bsMXthzYLbcngN4W2P8NtU9TWTdHC3HaQbjuuRfKKVdjVcLYP7G2qmyucMsEHVPA7DmQYw48pYtBq5Vc7YCYTqsGhMUWjqyyRq8Gpe6K44JAMEcrwoTmY?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Example 6: Curve of Intersection of a Cylinder and Plane]]></title><description><![CDATA[In this video I go over an example on determining the vector function of the curve of intersection between a vertical cylinder and a slanted plane. YouTube - Summary - Notes - Playlist - Vector Functions]]></description><link>http://direct.ecency.com/hive-111030/@mes/example-6-curve-of-intersection-of-a-cylinder-and-plane</link><guid isPermaLink="true">http://direct.ecency.com/hive-111030/@mes/example-6-curve-of-intersection-of-a-cylinder-and-plane</guid><category><![CDATA[hive-111030]]></category><dc:creator><![CDATA[mes]]></dc:creator><pubDate>Tue, 17 Jun 2025 18:26:30 GMT</pubDate><enclosure url="https://images.ecency.com/p/JLypLpqVPBaKaRaoubFyzF8ART61na2a8Kq4PUGKQePjzVsqLff6fgxyWcdFCg2dxmsuYf774kxNUYcxUy9Ei2knuPQWSPu25Rpv7vFHsoR42UELLVxzPxuTbGa2rxt73RPVqXqY3x7tRmvCgWtZCTrQ1ggLRKmAWWJy56Q1gHawT8EkxKQ9DTPig96k5kseP1?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[Rompecabezas de formas // Shapes-puzzle [ESP/ENG]]]></title><description><![CDATA[Shapes-Puzzle [ESP] ¡Hola a todos familia! Hoy quiero traerles un post diferente, les quiero contar algo más de mi. Soy profesor de matemática y siempre me intereso en todo lo que tenga que ver con en]]></description><link>http://direct.ecency.com/hive-148441/@n1t0/rompecabezas-de-formas-shapes-puzzle-espeng</link><guid isPermaLink="true">http://direct.ecency.com/hive-148441/@n1t0/rompecabezas-de-formas-shapes-puzzle-espeng</guid><category><![CDATA[hive-148441]]></category><dc:creator><![CDATA[n1t0]]></dc:creator><pubDate>Tue, 19 Jul 2022 05:02:24 GMT</pubDate><enclosure url="https://images.ecency.com/p/k75bsZMwYNu2L3iBMXq5y7xeiy1isFJsZxnMZSXuXEsxe4ee1cUkGyPgLqqbN9Up35UTGRJrXHohhKwdd8ivpnzfMLdY7H2FbT4a1YEHgGYoPNurctVZycgaA6j875tMrZrcfr4Y1nQLNKEQgiKYJajiJnag3mj26?format=match&amp;mode=fit" length="0" type="false"/></item><item><title><![CDATA[geogebra]]></title><link>http://direct.ecency.com/geogebra/@rnfcqmjryz/geogebra-qun50j</link><guid isPermaLink="true">http://direct.ecency.com/geogebra/@rnfcqmjryz/geogebra-qun50j</guid><category><![CDATA[geogebra]]></category><dc:creator><![CDATA[rnfcqmjryz]]></dc:creator><pubDate>Sun, 13 Jun 2021 12:50:45 GMT</pubDate></item><item><title><![CDATA[geogebra]]></title><link>http://direct.ecency.com/geogebra/@wsnnhup/geogebra-89cb1d000723c</link><guid isPermaLink="true">http://direct.ecency.com/geogebra/@wsnnhup/geogebra-89cb1d000723c</guid><category><![CDATA[geogebra]]></category><dc:creator><![CDATA[wsnnhup]]></dc:creator><pubDate>Sun, 13 Jun 2021 12:50:27 GMT</pubDate></item></channel></rss>