Vector Product

Simply perform the BXC operation.

Now,

for the x components, just change the sign of the y-component of the cross product of B and C
to negative. Now,we simply equate the x-component of AX(BXC) Just add (a_xb_xc_x - a_xb_xc_x) to the resulting x-component. Now take b_x and c_x common. Simply repeat the process to find the y components and the z components(for the y components, the sign of the z component of BXC is changed and for the z components, the sign of the x components of BXC is changed). If we once again take then we find that the formula is successfully derived.