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In the figure, the tip of $ c $ and the tail of $ d $ are both the midpoint of $ QR $. Express $ c $ and $ d $ in terms of $ a $ and $ b $.

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01:01

Wen Zheng

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 2

Vectors

Johns Hopkins University

Campbell 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.

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In the figure, the tip of …

02:58

In the figure, $D$ is the …

00:19

In the figure below, $B$ i…

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00:32

Given: $\square A B C D ; …

01:17

Two points are located at …

03:24

If $D$ is the midpoint of …

right. Victor C. And Victor de, In terms of vectors A and B know that this point em here is the midpoint, uh, the line segment joining Q and R. Okay, So first, if this was a and this was be and I formed a parallelogram, then Q r is this And then this is the other diagonal. And what's true is that diagonals of a parallelogram meat at the point at the midpoint of each or they bisect each other. So this is the point that's halfway between. So then, when you look at vector C, you couldn't see it's half of a plus B. Hey, subject er c equals half Victor's a plus beef. Well, all right, Now let's look at Victor D, which is right here. Somebody erased this picture. Start again. Okay, so here. Whoops. Here's a here's victor B And now what I'm gonna do is I'm gonna draw the opposite of a which is back here that's minus a. So if I draw that parallelogram, this is our This is our and this is the opposite of Q sort of. Okay, so here's that diagonal. There's this Diagon all and then here's vector D from here to here, which is coming from the mid point so half of minus a plus B

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