Question

If a,b,c,d be coplanar vectors, then show that (a×b)×(c×d)=0

Answer 1

Answer:

I assumed the four points A, B, C and D with position vector a, b, c and d to be on the x-y plane. So cross product between any of them is towards the z-axis. So I expanded the equation :

[a^b^d^]+[b^c^d^]+[c^a^d^]=[a^b^c^][a^b^d^]+[b^c^d^]+[c^a^d^]=[a^b^c^]

a^⋅(b^×c^)+b^⋅(c^×d^)+c^⋅(a^×d^)=a^⋅(b^×c^)a^⋅(b^×c^)+b^⋅(c^×d^)+c^⋅(a^×d^)=a^⋅(b^×c^)

Step-by-step explanation:

I hope it is helpful for you