The angle `theta` between the vector `p=hati+hatj +hatk` and unit vector along X-axis is

Options

A. `cos^(-1) ((1)/(sqrt3))`
B. `cos^(-1) ((1)/(sqrt2))`
C. `cos^(-1) ((sqrt3)/(2))`
D. `cos^(-1)((1)/(2))`

Answer

A

Explanation

The angle between
`p = hati + hatj + hatk `
`x -` axis ` x = hati`
is given by
`cos theta = (p * x)/(|p||x|) = ((hati + hatj + hatk))/(sqrt(1^(2) + 1^(2) + 1^(2)))((hati))/(sqrt(1^(2))) = (1)/(sqrt3)`
`implies theta = cos^(-1) ((1)/(sqrt3))`