Answer:
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:
