5 Difference between Dot Product and Cross Product (With Table)

Education has different fields that are taught to learners. The sciences, the languages, technicals, and humanities.

All sciences including Mathematics normally have some relationships. For instance, Mathematics and Physics have vector algebra as an integral part.

Vector is a physical quantity with both magnitude and direction while its counterpart scalar is a quantity that only has magnitude without direction.

Vector can be manipulated using two basic operations which are dot product and cross product. The two terms have been used interchangeably although they are different from each other.

So, what is the main difference between dot product and cross product? Dot product results in scalar quantity while cross product results in vector quantity.

For more information about the difference between dot product and cross product in tabular form, continue reading the article. You will also get to learn of the similarities between the two.

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Comparison Table (Dot Product vs. Cross Product)

Basic Terms	Dot Product	Cross Product
Meaning	It is a product of the magnitude of vectors and the cosine of the angle between them.	It is a product of the magnitude of vectors and the sine of the angle between them.
Resultant	It results in scalar quantity.	It results in vector quantity.
Direction	It does not have any direction.	It has direction.
Cumulative law	It strictly follows cumulative law.	It does not follow cumulative law strictly.
Position	When they are perpendicular to each other, the product is 0.	When parallel to each other the end product is 0.

What is Dot Product?

The dot product is a product of the magnitude of vectors and the cosine of the angle between them. The resultant of the dot product of vectors is a scalar quantity.

Scalar quantity only has magnitude but no direction hence dot product does not have direction. It is also known as scalar product or inner product or projection product.

The product is cumulative in nature, distributive, and follows scalar multiplication laws strictly. It is mainly used to define the length between two points in a plane when their coordinates are known.

The cosine is used so that the vectors may arrange themselves in the same direction. This makes it possible to obtain a projection of one vector over the other.

What is Cross product?

Cross product is a product of the magnitude of vectors and the sine of the angle between them. The resultant of the cross-product of vectors is a vector quantity.

Vector quantity has both magnitude and direction. It is known as a vector product. The results of the cross product of two vectors are always perpendicular hence the direction can be determined by the right-hand rule.

It does not follow cumulative law. It is also compatible with scalar multiplication law just as in dot product.

It is mainly used in computational geometry such as to define the distance between two skew lines. It is also used to determine if two vectors are coplanar or not.

Main Difference between Dot Product and Cross Product

Dot product results in scalar quantity while cross product results in vector quantity.
The dot product is the product of the magnitude of vectors and the cosine of the angle between them while the cross product is the product of the magnitude of vectors and the sine of the angle between them.
Dot products follow cumulative law strictly while cross-product does not follow cumulative law.
The dot product has no direction while the cross product has direction.
When the dot product is perpendicular to each other the result is 0 while when the cross product is perpendicular the result is not 0.

Similarities between Dot Product and Cross Product

They are both distributive over addition.
They both follow the scalar multiplication law.

Conclusion

Dot product and cross product are both operations used to manipulate vectors. They are both useful in spatial concepts

However, the two are different from each other. The main difference between the two is that dot product computes to a scalar quantity which generally has distance while cross-product computes to a vector quantity which has both distance and direction.

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