Vector u has its initial point at (15, 22) and its terminal point at (5, -4). Vector v points in a direction opposite that of u,

Question

3 years ago

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Vector u has its initial point at (15, 22) and its terminal point at (5, -4). Vector v points in a direction opposite that of u,

and its magnitude is twice the magnitude of u. What is the component form of v?
A. v=<-20, 36>
B. v=<-20, 56>
C. v=<20, 36>
D. v=<20, 52>

Mathematics

1 answer:

zzz [600] · Answer 1 · 2022-09-11T22:15:30+03:00

Answer:

D. v=<20, 52>

Step-by-step explanation:

Vector u can be written in component form by subtracting its initial point from its terminal point:

u = (5, -4) -(15, 22) = <-10, -26>

We are told that v = -2u, so ...

v = -2<-10, -26> = <20, 52>

_____

Multiplying a vector by -1 reverses its direction; multiplying it by some factor k changes its magnitude by a factor of k. To reverse the direction and double the magnitude, we can multiply u by -2.