Find a unit vector #bbhatu# in the direction opposite to #⟨−3,−9,−9⟩#?

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Answer 1 · 2018-08-11T22:23:34

#hat(u) = 1/sqrt(19) < 1, 3, 3 > = < sqrt(19)/19, (3sqrt(19))/19, (3sqrt(19))/19 >#

Given:

#< -3, -9, -9 >#

The vector of the same magnitude in the opposite direction is:

#< 3, 9, 9 >#

A smaller vector in the same direction is:

#1/3 < 3, 9, 9 > = < 1, 3, 3 >#

Then:

#abs(abs(< 1, 3, 3>)) = sqrt(1^2+3^2+3^2) = sqrt(1+9+9) = sqrt(19)#

So the unit vector in the same direction is:

#hat(u) = 1/sqrt(19) < 1, 3, 3 > = < sqrt(19)/19, (3sqrt(19))/19, (3sqrt(19))/19 >#