If `vecA = vecB + vecC` and the magnitudes of `vecA, vecB and vecC` are 5,4 and 3 units respecetively, the angle between `vecA` and `vecC` is :

Options

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

Answer

A

Explanation

`vecC + vecB = vecA`
`rArr " "vecB = vecA - vecC`
`" "|vecB|=|vecA - vecC|`
`" "4=sqrt(5^(2) + 3^(2) - 30 cos theta)`
`" "16-34 =-30cos theta`
`" "(-18)/(-30) =cos theta" "rArr" "cos theta= (3)/(5)`
`" " theta = cos ^(-1).(3)/(5)`