Use properties of the cross product to calculate the following:

Question

Use properties of the cross product to calculate the following:

 

(a) (e1+e2)×(e1×e2) =

 

(b) 3e3×(e3+e2) =

Answer 1

(a)

 

A x A = 0 for any vector A, so the answer to (a) is the zero vector

 

(b)

 

3e₃ x (e₃ + e₂) = 3(e₃ x e₃ + e₃ x e₂) = 3(0 - e₁) = -3e₁