Find two vectors in opposite directions that are orthogonal to the vector u. (There are many correct answers)

Question

u= 1/3i-3/8j

Vector in quadrant I

v=

Vector in Quadrant III

v=

Answer 1

For v to be perpendicular to u, the dot product must be zero.

If v = xi + yj, then u•v = x/3-3y/8 --> x = 9y/8.

Let y = 8 and x = 9(8)/8 = 9

In Quadrant I, v = 9i + 8j

In Quadrant III, v = -9i-8j

Check: u•v = 9/3 - 3(8)/8 = 3-3 = 0