# Thread: The Vector Product Problem

1. ## The Vector Product Problem

Im stuck on the following question

Find the value of for which (1, A , 3) and ( A, 2, 1) are orthogonal. Using that
value of A, find a third vector orthogonal to both of them.

iv done the cross product on them and got the following result (A+6)i - (1-3A)j + (-2-$\displaystyle A^2$)k but cant see anyway to actually determine A.

Thanks for any help

2. Originally Posted by jordanrs
Im stuck on the following question

Find the value of for which (1, A , 3) and ( A, 2, 1) are orthogonal. Using that
value of A, find a third vector orthogonal to both of them.

iv done the cross product on them and got the following result (A+6)i - (1-3A)j + (-2-$\displaystyle A^2$)k but cant see anyway to actually determine A.

Thanks for any help
You don't use the cross product. You use the dot product.

If two vectors are perpendicular (orthogonal) then their dot product is 0.