Question

If A and B are non-zero vectors, is it possible for A×B and A·B both to be zero?​

Answer 1

Answer:I believe this would make your two vectors both orthogonal and parallel, so no.

We define the cross product of vectors A and B to be the vector that makes a 90 degree angle with both A and B. If this vector is 0, then the vectors must be parallel and therefore never touch.

This already contradicts the dot product being zero, since A and B would have to make a 90 degree angle with each other while being parallel, which is absurd.

Explanation: