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One common term that you must have heard in mathematics is “Vectors”. Vectors can be both added and multiplied. Two ways for the multiplication of vectors are known as ‘Dot product” and “.cross product”. There is a lot of confusion between the difference between Dot Product and Cross Product.
This blog gives detailed information on the difference between Dot product and a cross product, based on its definition, formula, result, and usage.
Table of Contents
What is Dot Product?
The dot product is defined as the sum of the products of the corresponding entries of the two sequences of numbers. It is also known as the scalar product.
Through Geometric means, it means, Euclidean magnitudes and the cosine of the angle between them.
What is Cross Product?
The cross-product is a mathematical operation between two vectors in three-dimensional space. It is calculated by the right-hand rule.
The direction of the cross product of two non-zero parallel vectors, a and b, is given by the right-hand thumb rule.
Also Read: Difference Between Parallel and Perpendicular
Dot Product and Cross Product Formulas
The below-mentioned formulae are for Two vectors A and B. “N” signifies the perpendicular between A and B vectors.
Dot Product
A · Β = |A| |B| cos θ
Cross Product
A × Β = |A| |B| sin θ n
What is the Difference between Dot Product and Cross Product?
The basic difference between Dot Product and Cross Product is based on its application of dimensional figures. Cross Product is only applicable for 3-dimensional figures, whereas Dot Product is applicable for any dimensional figures.
Here are the other basics for differentiation:
Dot Product and Cross Product Chart
| Particulars | Dot Product | Cross Product |
| Definition | Product of magnitude of vectors and cos of the angle between them. | Product of magnitude of vectors and sine of the angle between them. |
| Formula | A · Β = |A| |B| cos θ | A × Β = |A| |B| sin θ n |
| Result | Scalar quantity. | Vector quantity |
Also Read: Chain Rule Questions and Answers
FAQ’s
The main difference between dot product and cross product is that cross product only works for 3D while dot product applies to any dimension.
The formulae for dot product in two vectors is |a||b| cos θ.
The formulae for cross-product is 个个 A x B = ab sin o n.
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