Question

30. Find the vector v with the given magnitude and the same direction as u.
which v=3 and u=(4,-4)

Answer 1

So we want a vector, v, that looks like this:


where the y component is the negative x component

Answer 2

if the magnitude is 3, then \[v_x^2 + v_y^2 = 3^2\]
we also know that
\[v_x =-v_y\]

Answer 3

so:
\[2v_x^2 = 9\]

Answer 4

therefore:
\[v_x = \sqrt{9/2}\]

Answer 5

and:
\[v_y = -\sqrt{9/2}\]