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Problem 7 Easy Difficulty

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 $.

Answer

$$
\mathbf{c}=\frac{1}{2} \mathbf{a}+\frac{1}{2} \mathbf{b} \quad \mathbf{d}=\frac{1}{2} \mathbf{b}-\frac{1}{2} \mathbf{a}
$$

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Video Transcript

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