What is the difference between a scalar product and a vector product, and how do I know which one to use in questions?

The main thing to consider here is the output of the operation. Vector and scalar products are both operations in which you take two vectors but then get something else. In a scalar product, you get a number out (like 1, 2, 3...). On the other hand, a vector product gives you a vector after you have done the operation.Both operations may help you determine the angle between two vectors, but everyone will agree that the scalar product is a much easier way of doing it, and most questions involving the scalar product ask you to compute angles! In general, the question will give you a hint as to which one to use. For example, many A-level papers have questions such as: ' Show that vectors a and b are perpendicular...''Find the equation of the plane through vectors a and b...'The first statement involves an angle, since it is asking to show that things are perpendicular. This is the kind of question where you'd like to use the scalar product. On the other hand, the second question asks you to find a plane, for which you need the normal vector: this is the sort of question where you'd like to use the vector product!