Use a specific example to prove that the cross product is also not associative. That is, use three specific vectors in 3-space to show that Vector a×(Vector b × Vector c) is not equal to (Vector a × Vector b) × Vector c.

Question

Use a specific example to prove that the cross product is also not associative. That is, use three specific vectors in 3-space to show that Vector a×(Vector b × Vector c)   is not equal to  (Vector a × Vector b) × Vector c.

Can you help me think of an example im having trouble doing so

Steve · Answer

come on. You can do a cross product, right? So, pick some vectors and do the math.

For example, let

u = <1,1,1>
v = <1,-1,1>
w = <2,1,3>

(uxv)xw = <2,0,-2>x<2,1,3> = <2,-10,2>
ux(vxw) = <1,1,1>x<2,-1,3> = <4,-1,-3>