Question

If dot product of two non zero vectors A and B is zero then magnitude of their cross product is

Answer 1

Explanation:

Dot product of two non zero vectors can be zero when value of Cos theta is zero or angle is 90

so their cross product is ABSin90 which is equal to AB as Sin90 =1

Answer 2

Magnitude of cross-product is zero.

Given:

A and B are non-zero vectors

A·B = 0

To find: |A×B|

Solution:

We know that

A·B = |A||B|cosθ

|A||B|cosθ = 0 (given)

But A and B are non-zero

⇒ cosθ = 0

⇒ θ = 90°

Now,

A×B = |A||B|sinθn

⇒ |AxB| = |A||B|sinθ

⇒ θ = 90

⇒ sinθ = sin90° = 0

⇒ |A×B| = 0

∴ Magnitude of cross product is zero.

SPJ2