Question

Why is the dot product of two vector quantities is always a scalar quantity?​

Answer 1

The dot product of two vectors (displacement and force, here) is always a scalar quantity. So, work done, or energy expended, is a scalar quantity. ... That's because it only matters whatever work is done by one in the direction of the other.

Answer 2

The dot product of two vectors is defined as the product of their magnitude with cosine of the angle between them.

Thus, if two vectors A and B having angle theta between them, then their scalar product is written as.

A • B = AB CosØ ( Scalar quantity).

Some important points :-

1. A • B = B • A

2. A • ( B+C) = A•B + A•C

3. A • A = A²

4. A • B = A (B cosØ)

5. i • i = j • j = k • k = 1

6. i • j = j • k = k • i = 0

7. cosØ = A • B/ AB