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 vecb and vecr.veca =0` then find the value of `vecr .vecb`.

Options

A. `4`
B. `8`
C. `6`
D. `9`

Answer

D

Explanation

We have
`vecrxxvecb=veccxxvecb`
`implies(vecr-vecc)xxvecb=vec0`
`impliesvecr-vecc` is parallel to `vecb`
`impliesvecr-vec=lamdavecb` for some scalar `lamda`
`impliesvecr=vecc+lamdavecb`……………i
`impliesvecr.veca=vecc.veca+lamda(vecb.veca)`
`=0=vecc.veca+lamda(vecb.veca) [ :' vecr.veca=0]`
`implieslamda=-(veca.vecc)/(veca.vecb)`
Substituting the value of `lamda` in (i) , we get
`vecr=vecc-(veca.vecc)/(veca.vecb)vecb`
`impliesvecr.vecb=(vecc.vecb)-(veca.vecc)/(veca.vecb)(vecb.vecb)impliesvecr.vecb=1-((-4))/1xx2=9`