Question

What is the difference between a scalar, a vector and a unit vector? Can we take the product of two unit vectors?

Answer 1

Hint: There are many quantities in physics which have only magnitude. Suppose, work done by a body is an example which only depends on the magnitude of doing work by that body. Magnitude can either be zero, positive or negative. Some quantities have direction as well. These quantities depend both on the magnitude as well as direction.

Complete step by step answer:
Let us understand these three things:
Scalar: Volume, density, speed, energy, mass, and time are examples of scalars, which are physical quantities that are completely characterized by their magnitude. Other quantities, like force and velocity, are called vectors because they have both magnitude and direction.
Vectors: A directed line segment whose length denotes the magnitude and whose orientation in space represents the direction is commonly used to express a quantity having magnitude and direction.
Unit vector: A vector is a quantity that has both a magnitude and a direction associated with it. A unit vector is a vector with a magnitude of one. It's also referred to as a Direction Vector.
Also, yes, we can take the product of two unit vectors. There can be two possibilities. If we take the product of two vectors to get the scalar value, we use the dot product method and to get the product as a vector form we use the cross product method.

Note: There are many physical quantities in physics which depend on the product of these two quantities of scalar and vector. The type of product we take decides what result we require. If we are required to get the value of torque which is a vector quantity, we need to get the cross product values of force and the displacement vector of the force of the point from which we are trying to find the value of torque.