Vector `P=6hati+4sqrt(2)hatj+sqrt(2)hatk` makes angle from Z-axas equal to

Options

A. `cos^(1)(sqrt((2)/(5)))`
B. `cos^(-1)(2/sqrt(2))`
C. `cos^(-1)((2sqrt2)/(5))`
D. None of these

Answer

C

Explanation

(c) `P=6hat(i)+4sqrt(2)hat(j)+4sqrt(2)hat(k)` ltbr gt Let P makes angle `gamma` from Z-axis,
`:.gamma=cos^(1)(P_(z)/(P))`
Here, `P_(z)=4sqrt(2)andP=sqrt((6)^(2)+(4sqrt(2))^(2)+(4sqrt(2))^(2))=10`
`:.gamma=cos^(-1)((4sqrt(2))/(10))=cos-(1)((2sqrt(2))/(5))`