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Figure 16 gives a geometric demonstration of Property 2 of vectors. Use components to give an algebraic proof of this fact for the case $ n = 2 $.

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$$\therefore a+(b+c)=(a+b)+c$$

03:03

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 2

Vectors

Missouri State University

Campbell University

Harvey Mudd College

Idaho State University

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.

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Figure 16 gives a geometri…

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$$\begin{array}{l}{\text {…

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Prove for vectors $\mathbf…

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Proof Prove that if $\math…

for the given problem, we want to demonstrate property to of vectors. So we have a let's say this is vector A. This is gonna be vector B. And this will be a vector C. So when we have a plus B1st, since this is A. And this is B. And their head to tail. We can always rearrange factors to be head details. So we can just skip that first step. So we know that A plus B is going to be this factor right here, and now we have A plus B. So it's gonna be this fact right here. And now we have plus C. So the A plus B plus C where we see this one's also had detail. So then that means that this new vector is going to be right here. So that's A plus B plus C. Now let's do it the other way. What if we had a B plus C first? Well, that's going to be this factor right here. And then we have a plus B plus C. So that's gonna be this vector right here. And as we see, it's the exact same thing

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