What is the anlge between a vector `vec A = 4 hati+3hatj+5hatk` and the x-axis ?

Options

A. `cos^(-1)""((3)/(5))`
B. `cos^(-1)""((2sqrt(2))/(5))`
C. `cos^(-1)""((3)/(sqrt(5)))`
D. `cos^(-1)""((2)/(5))`

Answer

B

Explanation

`A = sqrt(4^(2)+3^(2)+5^(2))=sqrt(50) =5sqrt(2)`
The angle between `vec A` and x-axis is given by
`cos alpha = (A_(x))/(|A|)=(4)/(5sqrt(2)) =(2sqrt(2))/(sqrt(5))`
`therefore alpha = cos^(-1)""((2sqrt(2))/(sqrt(5)))`