Question

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

Answer 1

`\binom{ (7 √(58) )/(58) }{ ( - 3 √(58) )/(58) }`

Step-by-step Step-by-step explanation:

First, find the magnitude of the vector:

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

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

`unit \: vector = \binom{ (7)/( √(58) ) }{ ( - 3)/( √(58) ) } \\ = \binom{ (7 √(58) )/(58) }{ ( - 3 √(58) )/(58) }`