If for a unit vector `a.(x-a).(x+a)=12`, then |x| is equal to

Options

A. 4
B. 2
C. `sqrt(13)`
D. `sqrt(11)`

Answer

C

Explanation

Given |a|=1
[` :'` It is a unit vector, mangnitude of unit vector is 1 ]
` therefore (x-a).(x+a)=12`
`implies x.x+x.a-a.x-a.a=12`
`[ :' a.a =|a|^(2) and a.b=b.a]`
`implies |x|^(2) -|a|^(2) = 12 implies |x|^(2) -1^(2) =12`
`[ :' |a|=1 ` as it is unit vector ]
` | x|^(2) = 13 gt |x|= sqrt(13)`