Question

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

Answer 1

`- (29)/(866) √(866) i + (5)/(866) √(866) j`

Step-by-step 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| = √( 216.5) = ( √(866) )/(2)`

The unit vector in the direction of this vector is

`= (v)/( |v| )`

`= - (14.5)/( ( √(866) )/(2) ) i + (2.5)/( ( √(866) )/(2) ) j`

`= - (29)/(866) √(866) i + (5)/(866) √(866) j`