What is the real life utility dot product and cross product of vectors? 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.
 A: For Scalar Product:
Energy and momentum fields have many applications for it. For example work done by a non-conservative force is given as $\vec{F}.\vec{d}$ etc
For Vector Product:
Rotational Mechanics  Uses much of it for example calculating angular momentum $\vec{L}=\vec{r}\times\vec{p}$ or Torque , $\vec{\tau}=\vec{r}\times\vec{F}$
A: I'm confused by what your teacher means by real life utility. I'm afraid the vast majority of humans get by perfectly fine without needing the dot or cross product. If he's asking how it pertains to geometry, the dot product is like shining a lamp on one [normed] vector perpendicularly and measuring the shadow of another, different [normed] vector on it. 
The cross product gives you the positive area of a parallelogram with a side being one vector, and the other being the other vector.
A: In everyday life, whenever we move to arrive somewhere we  instinctively use dot products to decide on the route, searching for the shortest.Pythagoras theorem is a dot product, and we use it all the time whether we know about it or not.
From the time of invention of the wheel,intuitive  knowledge of the cross product controls the use  of it , possibly also using sails needs the same intuition, where a push has unexpected consequences because of angular momentum.
A: A few roughly mentioned by our teacher:
1-The cross product could help you identify the path which would result in the most damage if a bird hits the aeroplane through it.
  The dot product could give you the interference of sound waves produced by the revving of engine on the journey.
2-solar panels need to be installed carefully depending upon angle of tilt of roof so that maximum electrical power is produced. it requires working out on direction and elevation of sun from roof, tilt angle followed by the product of these vectors.
3-We can assign a vector to each streamline of water moving in different directions under pressure from a faucet; and determine how much water is being lost by taking dot product of those vectors.
