The magnitude of the scalar p for which the vector `p(-3hat(i)-2hat(j)+13 hat(k))` is of unit length is :

Options

A. `1//8`
B. `1//64`
C. `sqrt(182)`
D. `(1)/(sqrt(182))`

Answer

D

Explanation

Let `vec(a)=p(-3hat(i)-2hat(j)+13hat(k))`
`=(-3p)hat(i)+(-2p)hat(j)+(13p)hat(k)`
It is given that `vec(a)` is of unit length
`:. |vec(a)|=1 rArr |vec(a)|^(2)=1`
`rArr (-3p)(-3p)+(-2p)(-2p)+(13p)(13p)=1`
`9p^(2)+4p^(2)+169p^(2)=1`
`rArr p^(2)=(1)/(182)rArr p = (1)/(sqrt(182))`