Question

Find a nonzero vector u with initial point P(-1, 3, -5) such that u has the same direction as v = (4, 2, 5). Suppose that the first component of u is u1 = 8

Answer 1

This is BS. There's no actual significance of the initial point.

Answer 2

Basically, a vector \(\langle a,b,c\rangle \) and a vector \(\langle na, nb, nc\rangle\) have the same direction. It's just that the second vector's magnitude is \(n\) times the first.

You will have to use that fact here.

Answer 3

You are given that \(\langle 4,2,5\rangle \) and \(\langle 8, x_0 , y_0\rangle \) have the same direction.

Answer 4

Do you see how the vector \(\langle 2\times 4 , 2 \times 2, 2 \times 5\rangle \) has the same direction as \(\langle 4,2,5\rangle\)?

Answer 5

ok i get it you use u=kv, since u=8 you can now solve k which is 8,4,10? :)

Answer 6

Precisely!

Answer 7

thank you :D