Properties of Scalar Product
- Scalar product of two vectors is always a real number (scalar).
- Scalar product is commutative i.e. a.b =b.a= |a||b| cos α
- If α is 90° then Scalar product is zero as cos(90) = 0. So, the scalar product of unit vectors in x, y directions is 0.
- If α is 0° then the scalar product is the product of magnitudes of a and b |a||b|.
- Scalar product of a unit vector with itself is 1.
- Scalar product of a vector a with itself is |a|2
- If α is 1800, the scalar product for vectors a and b is -|a||b|
- Scalar product is distributive over addition
a.(b + c) = a.b + a.c
- For any scalar k and m then,
la.(m b) = km a.b
- If the component form of the vectors is given as:
a = a1x + a2y + a3z
b = b1x + b2y + b3z
then the scalar product is given as
a.b = a1b1 + a2b2 + a3b3
- The scalar product is zero in the following cases:
- The magnitude of vector a is zero
- The magnitude of vector b is zero
- Vectors a and b are perpendicular to each other
Dot and Cross Products on Vectors
A quantity that is characterized not only by magnitude but also by its direction, is called a vector. Velocity, force, acceleration, momentum, etc. are vectors.
Vectors can be multiplied in two ways:
- Scalar product or Dot product
- Vector Product or Cross product
Table of Content
- Scalar Product/Dot Product of Vectors
- Projection of one vector on other Vector
- Properties of Scalar Product
- Inequalities Based on Dot Product
- Cross Product/Vector Product of Vectors
- Properties of Cross Product
- Cross product in Determinant Form
- Dot and Cross Product
- FAQs on Dot and Cross Products on Vectors