Let `veca = 2i + j + k, and b = i+ j ` 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

`|(veca xxvecb)xxvecc|=|vecaxxvecb||vecc|sin30^(@)`
`=1/2 (vecp +vecq+vecr)a^(2)`
`or vecx=1/2 (vecp +vecq +vecr)`
we have `veca = 2hati+hatj -2hatk and vecb = hati+hatj`
`Rightarrow vecaxx vecb = 2hati -2hatj+hatk`
`or |veca xx vecb|=sqrt9=3`
Also given `|vecc-veca|^(2)=8`
`or |vecc|^(2)=|veca|^(2)-2veca.vecc=8`
Given `|aveca|=3 and veca. vecc =|vecc|` , using these we get
`|vecc|^(2) -2|vecc|+1=0`
`or (|vecc|-1)^(2)=0`
`or |vecc|=1`
Substituting values of `|veca xx vecb|and |vecc|` in (i), we get
`|(veca xx vecb)xxvecc|=1/2xx 3xx 1= 3/2`