`veca =1/sqrt(10)(3hati + hatk)` and `vecb =1/7(2hati +3hatj-6hatk)`, then the value of `(2veca-vecb).[(vecaxxvecb)xx(veca+2vecb)]` is:

Options

A. `-5`
B. `-3`
C. `5`
D. `3`

Answer

A

Explanation

Clearly `veca` and `vecb` are perpendicular unit vectors.
Now,
`(2veca-vecb).{(vecaxxvecb)xx(veca+2vecb)}`
`=[2veca-vecb, vecaxxvecb,veca+2vecb]`
`=-[vecaxxvecb, 2veca-vecb, veca+2vecb]`
`=-(vecaxxvecb).{(2veca-vecb)xx(veca+2vecb)}`
`=-(vecaxxvecb).5(vecaxxvecb)`
`=-5|vecaxxvecb|=-5|veca|^(2)|vecb|^(2) [ :' veca_|_vecc]`
`=-5 [ :' |veca|=|vecb|=1]`