If `a=hati+2hatj+3hatk` and `b=hatixx(axxhati)+hatjxx(axx hatj)+hatk+(a xx hatk)`, then length of b is equal to

Options

A. `sqrt(12)`
B. `2sqrt(12)`
C. `3sqrt(14)`
D. `2sqrt(14)`

Answer

B

Explanation

We have , `a=hat(i)+2hat(j)+3hat(k)`
`b=hat(i)xx(axxhat(i))+hat(j)xx(axxhat(j))+hat(k)xx(axxhat(k))`
Now , `hat(i)xx(axxhat(i))=(hat(i).hat(i))a-(hat(i).a)hat(i)`
`=a-a_(1)hat(i)" "["let" (a=a_(1)hat(i)+a_(2)hat(j)+a_(3)hat(k))]`
Similarly , `hat(j)xx(axxhat(i))=a-a_(2)hat(j) and hat(k)xx(axxhat(k))`
`therefore b=3a-a=2a=2(hat(i)+2hat(j)+3hat(j))`
`rArr |b|=sqrt(4+16+36)=sqrt(56)=2sqrt(14)` .