Question

find the vector v with the given magnitude and the same direction ||v||=10, u=2i-3j

Answer 1

Hint:
vector is parallel to u, that means your vector is of the form ku, where k is any constant.

Answer 2

Find unit vector of "u" then multiply vector by ||v||
\[||u|| = \sqrt{2^{2}+(-3)^{2}} = \sqrt{13}\]
unit vector:
\[\frac{2}{\sqrt{13}}i - \frac{3}{\sqrt{13}}j\]
multiply by 10:
\[v = \frac{20}{\sqrt{13}}i - \frac{30}{\sqrt{13}}j\]
rationalize denominators
\[v = \frac{20\sqrt{13}}{13}i - \frac{30\sqrt{13}}{13}j\]