Question

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?

Answer 1

Though the vectors are going in opposite directions, their terminal and starting points are the same, just switched, check the picture below.

recall the component for (a,b), (c,d) is just (c-a , d-b), 

the component form for "v" is then

(5, -4), (15, 22) => (15 - 5, 22-(-4)) => (15 - 5, 22+4) => (10 , 26).

and since "v" is twice as long as "u", then its form is 2v, or

2(10 , 26) => (20, 52)