Question

Proof a•(b•c)=(a dot c)b-(a dot b)c

•=cross product

dot=dot product

Answer 1

This is known as vector triple product.

Which we can write it as:

We can let

On taking L.H.S of given equation:

We can simplify term inside the bracket as:

  

So

we can solve it for i component of this vector as:

So i component of given vector is:

On Adding and subtracting in this ,

So we will have:

  

This is same as i component of vector  

Similar expression we can obtain for j and k components.

So we can write: