Three vectors `vec(A),vec(B)` and `vec(C)` are such that `vec(A) = vec(B)+vec(C)` and their magnitude are 5,4 and 3 respectively. Find the angle between `vec(A)` and `vec(C)`.

Options

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

Answer

B

Explanation

The magnitudes of A, B and C= 5: 4: 3.

The vectors form a right angled triangle.
`because 5x^(2)=4x^(2)+3x^(2)`
Let `theta` be the angle between A and C.
`therefore sin theta =(4)/(5) therefore theta = sin^(-1)""(4)/(5)`