Question

How do you find the unit vector in the direction of the given vector 6i-2j?

Answer 1

`(3sqrt(10)/10)hati - (sqrt(10)/10hatj)` Please read the explanation.

Explanation:

Divide the given vector by the magnitude:

`|6hati - 2hatj| = sqrt(6^2 + (-2)^2) = 2sqrt(10)`

`(6hati - 2hatj)/(2sqrt(10)) = (3sqrt(10)/10)hati - (sqrt(10)/10)hatj)`

Please observe that the magnitude of the resulting vector is 1:

`sqrt((3sqrt(10)/10)^2 + (- (sqrt(10)/10)hatj)^2) = 1`