The vectors `a=2hati+hatj-2hatk, b=hati+hatj`. If c is a vector such that `a.c=|c| and |c-a|=2sqrt2,` angle between `axxb` and c is `45^(@)`, then `|(axxb)xxc|` is

Options

A. 3
B. `(sqrt3)/(2)`
C. `(3sqrt2)/(2)`
D. None of these

Answer

C

Explanation

Now, `|a|^(2)=9 and |b|^(2) = 2 `
`therefore |c-a|^(2) =|c|^(2) +|a|^(2) -2c*a=8`
`=|c|^(2)+9-2|c| =8 rArr |c| = 1`
Now , ` a xx b = | (hati , hatj , hatk ) , ( 2, 1 , -2), (1, 1 , 0)|=2 hati - 2 hatj+ hatk `
` rArr | a xx b| = sqrt( 2^(2) +(-2)^(2)+1^(2))=3`
`therefore |(a xx b) xx c|=|a xx b||c|sin 45^(@) = 3(1) ((1)/(sqrt(2)))=(3sqrt(2))/(2)`