Today, my teacher asked us what is the real life utility of the dot product and cross product of vectors. Many of us said that one gives a scalar product, and one gives a vector product. But he said that, that was not the real life utility of the dot and cross product. He asked us, "Students, why do we have to learn these two concepts? Because they are given in the book? Or because they are important concepts of vectors, or refer do they have some actual utility." None of us could answer. Does anyone here know a proper answer to an improper question like this? N.B.: Please pardon me if it's a foolish question, and don't give me credit if it opens up a huge set of answers.