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=<4,5,0>
Q=<1,0,3>
C=PxQ
Cross product is the expansion of the following determinant:
Det
i j k
4 5 0
1 0 3
= <5*3-0*0, -(4*3-1*0), 4*0-1*5 >
= <15,-12, -5>

Check orthogonality (dot products = 0)
C.P=<15,-12,-5>.<4,5,0>=60-60-0=0
C.Q=<15,-12,-5>.<1,0,3>=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.