Dot and Cross Product
Some of the common differences between dot and cross product of vectors are:
| Property | Dot Product | Cross Product |
|---|---|---|
| Definition | a⋅b = |a| |b| cos θ, where θ is the angle between the vectors. | a×b = |a| |b| sin θ n̂, where θ is the angle between the vectors, and n̂ is a unit vector perpendicular to the plane containing a and b. |
| Result | Scalar | Vector |
| Commutativity | Holds [a⋅b = b⋅a] | Doesn’t hold [a×b = −(b×a)] |
| Direction | Scalar value, no direction | Perpendicular to the plane containing a and b |
| Orthogonality | Two vectors are orthogonal if their dot product is zero. | The cross product of two non-zero vectors is orthogonal to both of them. |
| Applications | Finding the angle between vectors, projection of one vector onto another | Finding torque in physics, determining normal vectors to surfaces |
Read More,
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