The direction cosines of `hati + hatj + hatk` are

Options

A. `1,1,1`
B. `2,2,2`
C. `(1)/(sqrt(2)),(1)/(sqrt(2)),(1)/(sqrt(2))`
D. `(1)/(sqrt(3)),(1)/(sqrt(3)),(1)/(sqrt(3))`

Answer

D

Explanation

Let `vecA = hati + hatj + hatk therefore A_(x) = 1, A_(y) = 1, A_(z) = 1`
and `A = sqrt(A_(x)^(2) + A_(y)^(2) + A_(z)^(2)) = sqrt((1)^(2) + (1)^(2) + (1)^(2)) = sqrt(3)`
`cos alpha, cos beta, and cos gamma` are the direction cosines of `vecA`.
`therefore cos alpha = (A_(x))/(A) = (1)/(sqrt(3)) , cos beta = (A_(y))/(A) = (1)/(sqrt(3)) , cos gamma = (A_(z))/(A) = (1)/(sqrt(3))`