Question

Two vectors `vec"A"` and `vec"B"` have equal magnitudes. If magnitude of `vec"A"` + `vec"B"` is equal to two times the magnitude of `vec"A"` - `vec"B"`, then the angle between  `vec"A"` and `vec"B"` will be ______.

Options

• `sin^-1(3/5)`

• `sin^-1(1/3)`

• `cos^-1(3/5)`

• `cos^-1(1/3)`

Answer 1

Two vectors `vec"A"` and `vec"B"` have equal magnitudes. If magnitude of `vec"A"` + `vec"B"` is equal to two times the magnitude of `vec"A"` - `vec"B"`, then the angle between  `vec"A"` and `vec"B"` will be `underlinebb(cos^-1(3/5))`.

Explanation:

Given `|vec"A"+vec"B"|=|vec"A"-vec"B"|xx2`

⇒  `|vec"A"+vec"B"|^2=|vec"A"-vec"B"|^2xx4`

⇒ `0=3|"A"|^2+3|"B"|^2-10|"A"||"B"|costheta`

⇒ `0 = 3|"A"|^2+3|"A"|^2-|10|"A"|^2costheta`

⇒ `|10||"A"|^2costheta=6|"A"|^2`

⇒ cos θ = `3/5`