The angle subtended by vector `vecA = 4 hati + 3hatj + 12hatk` with the x-axis is :

Options

A. `sin^(-1)""((3)/(13))`
B. `sin^(-1)""((4)/(13))`
C. `cos^(-1)""((4)/(13))`
D. `cos^(-1)""((3)/(13))`

Answer

C

Explanation

The angle made by the vector `vec A` with the x-axis is given by `cos theta =(Ax)/(A)`
But `A= 4 hati +3 hatj +12 hatk therefore Ax =4 and A = sqrt(4^(2)+3^(2)+12^(2)) = sqrt(169) =13`
`therefore cos theta =(4)/(13)" or "theta = cos^(-1)""((4)/(13))`