Question

If θ is the angle between the unit vectors `bar"a"` and `bar"b"`, the `cos theta = theta/2` = ______.

Options

• `1/2|bar"b" - bar"b"|`

• `1/2|bar"a" + bar"b"|`

• `|bar"a" - bar"b"|/|bar"a" + bar"b"|`

• `|bar"a" + bar"b"|/|bar"a" - bar"b"|`

Answer 1

If θ is the angle between the unit vectors `bar"a"` and `bar"b"`, the `cos theta = theta/2` = `1/2|bar"a" + bar"b"|`.

Explanation:

`(bar"a" + bar"b")*(bar"a" + bar"b") = |bar"a"|^2 + |bar"b"|^2 + 2bar"a"*bar"b"`

⇒ `|bar"a" + bar"b"|^2 = 2.2 cos^2 theta/2`

⇒ cos θ = `theta/2 = 1/2|bar"a" + bar"b"|`