Let `veca = 2hati + hatj + hatk, and vecb = hati+ hatj ` if c is a vector such that `veca .vecc = |vecc|, |vecc -veca| = 2sqrt2` and the angle between `veca xx vecb and vec is 30^(@)` , then `|(veca xx vecb)|xx vecc|` is equal to

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]`