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If $ A $, $ B $, and $ C $ are the vertices of a triangle, find $$ \vec{AB} + \vec{BC} + \vec{CA} $$

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01:06

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 2

Vectors

Johns Hopkins University

Missouri State University

Baylor University

University of Michigan - Ann Arbor

Lectures

02:56

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

11:08

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

01:20

If $A, B,$ and $C$ are the…

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Suppose $A, B,$ and $C$ ar…

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Consider a triangle whose …

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Suppose that $A, B,$ and $…

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00:32

Triangle ABC has vertices …

F a b b C. Um Or if Fabian's here advertises of a triangle. So let's say we have 00 23 and 50 for example. And we have these vortices of the triangle and we have three vectors adding them up. We want to know what the resulting vector is going to be. Well remember from vector addition that if we have this one is the head and now it's going from tail to head, we know that the resulting vector, if we had a to B Plus B two C, that would just be a to C. But keep in mind that A to see is the exact opposite of C. To A. So because of that, we see that A to see is a negative C. To A. So if we add negative C. A plus C. A, we end up getting zero. So this is true for all triangles. The some of the vectors would be zero.

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