Find two unit vectors that are perpendicular to both j + 2k and i − 3j + 4k. (Enter your answers as a comma-separated list.)

Question

I have tried multiple times. I got the cross product of the two vectors as: -2i +2j + k and then I found the magnitude of that which is sqrt17. But, I don't know if I am doing it correctly. Someone please help

Answer 1

The cross product of <0,1,2> and <1,-3,4> is <1*4 - 2(-3), -(0*4-2*1), 0(-3)-1*1> = <10, 2, -1>

This vector is perpendicular to the first two vectors.

To find the unit vector, we must divide this vector by its length.

U = <10, 2, -1>/√(105)

The second vector would be the same vector but pointing in the opposite direction. So we just change the signs.

V = <-10, -2, 1>/√(105)