U = <-6, 4, 2> = -6i + 4j + 2k, where i = <1,0,0>, j = <0,1,0>, and k = <0,0,1>
Similarly, V = <3,1,5> = 3i + j + 5k
A vector orthogonal to both U and V is the cross product, U x V.
U x V can be found by evaluating the "determinant" of the following "matrix":
i j k
-6 4 2
3 1 5
UxV = [(4)(5) - (2)(1)]i - [(-6)(5) - (2)(3)]j + [(-6)(1) - (4)(3)]k
= 18i + 36j -18k
= <18, 36, -18>
You can check that the dot product of U with UxV and the dot product of V with UxV are both zero. So UxV is orthogonal to both of U and V.
