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. `pi//2`
D. `sin^(-1)(3//4)`

Answer

C

Explanation

See the vector diagam given below OR =5 units
OP=4 units, OQ=3 units

As,
`5=sqrt(4^(2)+3^(2)+2xx4xx3xx cos theta)`
Taking square on both sides
`rArr 25=16+9+24 cos theta`
`rArr cos theta=0 rArr 90^(@) =(pi)/(2)`
Angle betwen A and C `=angle QOR`
`sin (angle QOR)=(4)/(5)`
`rArr angleQOR= "sin"^(-1)((4)/(5))`
Also, `cos (angleQOR)=(3)/(5)`
`rArr angle QOR="cos"^(-1)((3)/(5))`