Question

Find the unit vector in the direction of v=(7,-3). (enter exact answers with square roots)

Answer 1

Answer:

$\binom{ \frac{7 \sqrt{58} }{58} }{ \frac{ - 3 \sqrt{58} }{58} }$

Step-by-step explanation:

First, find the magnitude of the vector:

$|v| = \sqrt{( {(7)}^{2} + {( - 3)}^{2}) } \\ = \sqrt{(49 + 9)} \\ = \sqrt{58}$

Then, divide each component of the vector by the magnitude to get the unit vector and rationalise:

$unit \: vector = \binom{ \frac{7}{ \sqrt{58} } }{ \frac{ - 3}{ \sqrt{58} } } \\ = \binom{ \frac{7 \sqrt{58} }{58} }{ \frac{ - 3 \sqrt{58} }{58} }$