Find a unit vector bbhatu in the direction opposite to ⟨−3,−9,−9⟩?
1 Answer
Aug 11, 2018
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 >