Question

Find a unit vector in the same direction as the given vector: v = −14.5i + 2.5 j.

Answer 1

ANSWER

$- \frac{29}{866} \sqrt{866} i + \frac{5}{866} \sqrt{866} j$

EXPLANATION

The given vector is v = −14.5i + 2.5 j.

The magnitude of this vector is

$|v| = \sqrt{ {( - 14.5)}^{2} + {2.5}^{2} }$

$v| = \sqrt{ {( - 14.5)}^{2} + {2.5}^{2} }$

$v| = \sqrt{ 216.5} = \frac{ \sqrt{866} }{2}$

The unit vector in the direction of this vector is

$= \frac{v}{ |v| }$

$= - \frac{14.5}{ \frac{ \sqrt{866} }{2} } i + \frac{2.5}{ \frac{ \sqrt{866} }{2} } j$

$= - \frac{29}{866} \sqrt{866} i + \frac{5}{866} \sqrt{866} j$