Question

1. Let u (1.-3,2), v= (-1.4.2). Then find b) a unit vector in the same direction of 4v.

Answer 1

4v points in the same direction as v, so all you need to do is normalize v.

Simply multiply it by the reciprocal of its magnitude:

$v = (-1, 4, 2) \implies \|v\| = \sqrt{(-1)^2 + 4^2 + 2^2} = \sqrt{21}$

$\implies \dfrac{v}{\|v\|} = \dfrac{(-1,4,2)}{\sqrt{21}} = \left(-\dfrac1{\sqrt{21}}, \dfrac4{\sqrt{21}}, \dfrac2{\sqrt{21}}\right)$