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### Main Difference

The Dot and Cross product are most widely used terms in mathematics and engineering. They both have many applications. A Dot and Cross product vary largely from each other. The major difference between both the products is that dot product is a scalar product, it is the multiplication of the scalar quantities whereas vector product is the multiplication of vector quantities. their function can be understood either algebraically or mathematically. The dot product is known as scalar product whereas the cross product is known as vector product. they both vary in the calculation and their implemented applications. Basically, both these products are used to multiply vectors. if we take the dot product of vectors it will give scalar quantity on the other side we multiply vectors through the cross product it will give vector quantity.

### What is Dot Product?

In math concepts, the dot product or maybe scalar product happens to be algebraic operations which take a couple of equal-length patterns of quantities which are generally coordinate vectors and also returns one particular number, Or multiplication of two quantities resulting from a singular quantity is known as Dot product. Dot product takes place between two quantities. This kind of function could be characterized frequently either algebraically or even geometrically. Algebraically, this is basically the add up of the products from the related terms of these two patterns associated with numbers. Geometrically, it pertains to the product from the Euclidean magnitudes of these two vectors as well as the cosine of the angle between the two. The particular identity “dot product” hails from the focused dot ” • ” that is certainly generally employed to specify this kind of procedure, and the second term “scalar product” focuses on the fact that end result should be a scalar though it is the product of two vector quantities. In the three-dimensional area, the dot product differences with the cross product associated with 2 vectors, which usually generates a pseudo vector as the outcome. The dot product is proportional towards the cosine of the angle in between 2 vectors in Euclidean space associated with a variety of dimensions. when the dot product of two vectors is taken, it gives the magnitude of both the vectors plus the cosine of the angle between both of them.

### What is Cross product?

In physics or mathematics concept, the cross product or sometimes called vector product is usually a binary function of 2 vectors in the three-dimensional area (R*R*R) and is also symbolized by the mark “×”. Provided a couple of linearly independent vectors y and z, the particular cross product, y × z, can be described as a vector that is certainly verticle with respect to each and for that reason perpendicular to the plane including them. Cross product has numerous applications in mathematics, physics, engineering, and even in computer encoding. It shouldn’t be mistaken for dot product. If two vectors have a similar direction or maybe each one offers absolutely no length, consequently their particular cross product can be 0. A lot more, in general, the magnitude of the product equates to the region of the parallelogram using the vectors with regard to sides; particularly, the magnitude of the product associated with a couple of perpendicular vectors will be the product of their total lengths. The cross product can be anti-commutative (i.e. a × b = -b × a) and is also distributive over addition (i.e. a × (b + c) = a × b + a × c). The area R3 along with the cross product is definitely an algebra within the real quantities, which can be none commutative nor associative, however, is a Lie algebra using the cross product to be the Lie bracket.

### Key Differences

- Dot product gives scalar quantity whereas cross product gives vector quantity
- Dot product, the connections between similar dimensions whereas the connections.
- Dot product of quantities which are in the same direction is maximum whereas cross product of two entries in the same direction is zero
- Dot product of two quantities which are orthogonal to each other is zero whereas cross product is maximum
- dot product outcome does not specify direction whereas cross product specifies the direction
- The dot product is used for the projection of one vector on another but cross product is not used for this purpose.
- The dot product is “a .b” whereas the cross product is “a x b”
- Cross product is anticommutative whereas dot product is commutative