How do you find a unit vector in the same direction as a=(-10, 6, -7)?

1 Answer
Jun 13, 2017

Compute the magnitude and then divide each component by the magnitude.

Explanation:

Compute the magnitude:

#|veca|= sqrt((-10)^2+ 6^2+ (-7)^2)#

#|veca|= sqrt(100 + 36+ 49)#

#|veca|= sqrt(185)#

To obtain the unit vector of #veca = (-10, 6, -7)#, we divide each component by #sqrt185# but we should rationalize #1/sqrt185# to #sqrt185/185#:

#hata = ( (-10sqrt185)/185, (6sqrt185)/185, (-7sqrt185)/185)#