Question

If θ is the angle between any two vectors `bara` and `barb` and `|bara · barb| = |bara xx barb|` then θ is equal to ______.

Options

• 0

• `π/4  "or"  (3π)/4`

• `π/2`

• `pi  "or"  pi/6`

Answer 1

If θ is the angle between any two vectors `bara` and `barb` and `|bara · barb| = |bara xx barb|` then θ is equal to `underlinebb(π/bb4  "or"  bb(3π)/bb4)`.

Explanation:

`|bara · barb| = |bara xx barb|`

We know:

`|bara · barb| = |bara||barb| cosθ`

`|bara xx barb| = |bara||barb| sinθ`

So,

`|cosθ| = |sinθ| ⇒ tanθ = ± 1 ⇒ θ = pi/4  "or"  (3pi)/4`