Question

Can you have $\overrightarrow{A}\times \overrightarrow{B}=\overrightarrow{A}·\overrightarrow{B}$ with A ≠ 0 and B ≠ 0? What if one of the two vectors is zero?

Answer 1

No, we cannot have $\overrightarrow{A}\times \overrightarrow{B}=\overrightarrow{A}·\overrightarrow{B}$ with A ≠ 0 and B ≠ 0. This is because the left hand side of the given equation gives a vector quantity, while the right hand side gives a scalar quantity. However, if one of the two vectors is zero, then both the sides will be equal to zero and the relation will be valid.