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 `vecaxxvecb=2hati-2hatj+hatk`
`:.|(vecaxxvecb)xxvecc|=|vecaxxvecb||vecf|sin30^(@)=3/2|vecc|`
Now,
`|vecc-veca|=2sqrt(2)`
`implies|vecc-veca|^(2)=8`
`implies|vecc|^(2)+|veca|^(2)-2(veca.vecc)=8`
`implies|vecc|^(2)|9-2|vecc|=8`
`implies|vecc|^(2)-2|vecc|+1=0implies|vecc|=1`
Hence `|(vecaxxvecb)xxvecc|=3/2`