if vectors A&B are non zero vectors ,is it possible for their dot product and cross product to be zero? explain.

It can be proved that it’s impossible.

The dot product is defined as:

a⋅b=∥a∥∥b∥cos(θ)  

where  θ  is the angle between  a  and  b .

The cross product is defined as:

a×b=∥a∥∥b∥sin(θ)n^  

and the magnitude of this is given by:

∥a×b∥=∥a∥∥b∥sin(θ)  

We also know that:

cos2(θ)+sin2(θ)=1  

We can substitute the dot product and the magnitude of the cross product in here, to find:

(a⋅b)2+∥a×b∥2=∥a∥2∥b∥2  

We’ve specified that  a  and  b  are non-zero vectors, so the right hand side cannot be zero. As a result, at least one of  (a⋅b)2  or  ∥a×b∥2  must be non-zero.

Step-by-step explanation:

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