Find the cross product a ⨯

b. a = 4, 5, 0, b = 1, 0, 3 verify that it is orthogonal to both a and

b. (a ⨯

b.· a = (a ⨯

b.· b =

P=

Q=

C=PxQ

Cross product is the expansion of the following determinant:

Det

i j k

4 5 0

1 0 3

=

=

Check orthogonality (dot products = 0)

C. P=.=60-60-0=0

C. Q=.=15-0-15=0

Therefore both dot products equal zero, meaning that C is orthogonal to both P and Q, as the cross-product should behave.