Question

If θ is the angle between any two vectors `veca` and `vecb,` then `|veca.vecb| = |veca xx vecb|` when θ is equal to ______.

Options

• 0

• `pi/4`

• `pi/2`

• π

Answer 1

If θ is the angle between any two vectors `veca` and `vecb,` then `|veca.vecb| = |veca xx vecb|` when θ is equal to `underline(pi/4)`.

Explanation:

Let θ be the angle between two vectors `veca` and `vecb`.

Then, without loss of generally, `veca` and `vecb` are non-zero vectors, so that `|veca∣and |vecb|` are positive.

`|veca.vecb| = |veca xx vecb|`

⇒ `|veca||vecb|cosθ = |veca||vecb|`sinθ

⇒ cosθ = sinθ [`veca` and `vecb` are positive]

⇒ tanθ = 1

⇒ θ = `pi/4`

Hence, `|veca.vecb| = |veca xx vecb|` when θ is equal to `pi/4`.

The correct answer is `pi/4`.