Question

If `bar c = 3bara- 2bar b ` Prove that `[bar a bar b barc]=0`

Answer 1

Given `barc=3bara-2barb`

Prove that `[bar a bar b barc]=0`

`barb xxbarb = 0` If in a scalar triple product, two vectors are equal, then the secalar triple product is zero.

`L.H.S=[bara barb barc]`

`=bara (barbxxbarc)`

`=bara(barbxx(3bara-2barb))`

`=bara(3baraxxbarb-2barbxxbarb)`

`=bara(3baraxxbarb-0)`

`=2baraxxbaraxxbarb`

`=2xx0xxbarb`

`=0`

Hence Proved