If `vec(A)=vec(B)+vec(C )`, and the magnitudes of `vec(A)`,`vec(B)`,`vec(C )` are 5,4, and 3 units, then the angle between `vec(A)` and `vec(C )` is

Options

A. `cos^(-1)(3//5)`
B. `cos^(-1)(4//5)`
C. `sin^(-1)(3//4)`
D. `pi//2`

Answer

A

Explanation

Angle between `vec(B)` and `vec(C ) is 90^(@)`
`tan alpha = (B)/(C ) = (4)/(3)`
`sin alpha = (4)/(5)`
`cos alpha = (3)/(5) rArr alpha = cos ^(-1)((3)/(5))`