Let `veca=-hati-hatk,vecb =-hati + hatj and vecc = i + 2hatj + 3hatk` be three given vectors. If `vecr` is a vector such that `vecr xx vecb = vecc xx vecd and vecr.veca =0` then find the value of `vecr .vecb`.

Answer

9

Explanation

`vecr xx vecb = vecc xx vecb`
Taking cross product with `veca`
`vecaxx (vecrxxvecb)=vecaxx (veccxx vecb)`
`or (veca.vecb)vecr-(veca.vecr)vecb=vecaxx (vecc xx vecb)`
`vecr=-3hati+6hatj+3hatk`
`vecr.vecb = 3 + 6 =9`