Let `veca=2hati+hatj-2hatk` and `vecb=hati+hatj`. If `vecc` is a vector such that `veca.vec=|vecc|,|vecc-veca|=2sqrt(2)` and the angle between `vecaxxvecb` and `vecc` is `30^(@)`, then `|(vecaxxvecb)xxvecc|=`.

Options

A. `2//3`
B. `3//2`
C. `2`
D. `3`

Answer

B

Explanation

We have
`veca.vecc=|vecc|` and `|vecc-veca|=2sqrt(2)`
`implies veca.vecc=|vecc|` and `|vecc|^(2)-2(veca.vecc)=8`
`implies|vecc|^(2)+9-2|vecc|=8implies(|vecc|-1)^(2)=0implies|vecc|=1`
Now,
`|(vecaxxvecb)vecc)|=|vecaxxvecb||vecc|sin30^(@)`
`implies|(vecaxxvecb)xxvecc)| =1/2|vecaxxvecb|=3/2 [ :' vecaxvecb=2hati-2hatj+hatk]`