If `x hat(i)+ y hat(j)+zhat(k)` is a unit vector and `x:y:z=sqrt(3):2:3`, then what is the value of z?

Options

A. `(3)/(16)`
B. 3
C. `3/4`
D. 2

Answer

C

Explanation

Let `xhat(i)+yhat(i)+zhat(k)` is a unit vector.
`:.x^(2)+y^(2)+z^(2)=1`
Given `x:y:z=2k and z=3k`
`:. (sqrt(3)k)^(2)+(2k)^(2)+(3k)^(2)=1`
`rArr 3k^(2)+4k^(2)+9k^(2)=1`
`rArr k^(2)=(1)/(16)rArr k= (1)/(4)`
Hence, `z=3k=3xx(1)/(4)=(3)/(4)`