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

1 Answer
Aug 11, 2018

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

Explanation:

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 >