If `vec A=vec B + vec C,` and the magnitude of `vec A, vec B and vec C` are `5,4 and 3` units respectively. the angle between `vec A and vec C` is

Options

A. `theta = cos^(-1)""((2)/(5))`
B. `cos^(-1)""((3)/(5))`
C. `theta = cos^(-1)""((4)/(5))`
D. `cos^(-1)""((3)/(4))`

Answer

B

Explanation

`vec A = vec C + vec B" "[because 5^(2) =3^(2) +4^(2)]`
`vec A` is the resultant of `vec B and vec C and vec B` is perpendicular to `vec C`.

Angle between A and C is given by
`cos theta =(3)/(5) therefore theta = cos^(-1)""((3)/(5))`