Find a unit vector orthogonal to the vectors 6𝐢+7𝐣+2𝐤 and 4𝐢+7𝐣+7𝐤 with non‑negative first coordinate. (Write your solutions using the standard basis vectors 𝐢, 𝐣, and 𝐤)

Question

I need help approaching this problem!

Answer 1

Take the cross product of the two vectors det of matrix with rows i j k, 6 7 2, 4 7 7

Find the magnitude of the cross product = sqrt(a_x²+a_y²+a_z²) and divide all terms by this amount

Multiply all terms by -1 if the first term is negative