The value of `hat(i)xx(hat(i)xxa)+hat(j)xx(hat(j)xxa)+hat(k)xx(hat(k)xxa)` is

Options

A. a
B. `axxhat(k)`
C. `-2a`
D. `-a`

Answer

C

Explanation

(c) Suppose, `a=a_(1)hat(i)+a_(2)hat(j)+a_(3)hat(k)`
Now, `(hat(i)xxa)=a_(2)hat(k)-a_(3)hat(j)`
Now `hat(i)xx(hat(i)xxa)=-a_(2)hat(j)-a_(3)hat(k)`
Similarly, `hat(i)xx(hat(j)xxhat(a))=-a_(1)hat(i)-a_(3)hat(k)`
and `hat(k)xx(hat(j)xxa)=-a_(1)hat(i)-a_(2)hat(j)`
`:.hat(i)(hat(i)xxa)+hat(j)(hat(j)xxa)+hat(k)(hat(k)xxa)=-2a`