Find a unit vector that has the same direction as the vector a and the opposite direction of the vector a.

Question

Find a unit vector that has the same direction as the vector a and the opposite direction of the vector a.

a = −15i + 8j

(a) the same direction as the vector a

_________ i + _______ j

(b) the opposite direction of the vector a

___________ i +  ________j

Answer 1

To find the unit vector in the same direction, calculate the magnitude of this vector and divide the coefficients of i and j in the given vector by that number.

The unit vector in the opposite direction will have the coefficients of the unit vector above, both multiplied by -1.