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Scalar Product of Vectors

In this lesson on vector, we’ll talk about the scalar product of vectors.

How to represent scalar product in Math

We use a ⚫ to represent scalar product, hence, they are sometimes also called dot product.

Definition of scalar product

When we take the scalar product of vector a and b, we are essentially doing this:

formula for scalar product of vectors

Note that |a||b| cos θ gives a value (numerical value). Hence, the result of a scalar product is a numerical value.

Finding scalar product of vectors expressed in x, y, z- coordinates form

If the vectors are expressed in x, y, z- coordinates form, the scalar product could be found in this manner:

equation to find scalar product of dot product for vectors, when they are expressed in x,y,z- coordinates form

Useful results of scalar product

  1. Since the same vectors are parallel to each other, and hence angle between them is 0 (i.e. cos0ᵒ = 1) , a . a = |a|²
  2. Dot product of perpendicular vectors will give 0 (since cos 90ᵒ = 0).
  3. To find the angle between 2 vectors, we can use the formula cosθ = (a. b )/( |a| |b| )

Notes on H2 Math Vectors

You’ll find all the notes on H2 A Level Math Vectors topic here.

All the notes for H2 A Level Math

Go here to find all the notes and resources for H2 A level Math.

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