## Cross Product Calculator

If a = (a1, a2, a3) and (b1, b2, b3), then the cross product of a and b is the vector a X b = (a2b3 — a3b2, a3b1, — a1b3, a1b2 — a2b1)
The cross product a x b of two vectors a and b, unlike the dot product, is a vector. For this reason it is sometimes called the vector product.

##### Cross Product Calculator

Enter the components of each of the two vectors, as real numbers

Please fill all fields as number

Cross Product Calculator is a free online tools that displays the cross product of two vectors. online cross product calculator tool makes the calculation faster, better, very easy and it displays the cross product in a fraction of seconds.

## Cross Product Formula:

The formula for the cross product in terms of components. Since we know that i×i=0=j×j and that i×j=k=−j×i, this quickly simplifies to a×b=(a1b2−a2b1)k=|a1a2b1b2|k

## How to Use the Cross Product Calculator?

The procedure to use the cross product calculator is as follows:

Step 1: Enter the real numbers in the respective input field

Step 2: Now click the button “Solve” to get the cross product

Step 3: Finally, the cross products of two vectors will be displayed in the output field

## Definition of the Cross Product

The vector or cross product of two vectors is written as AxB and reads "A cross B." It is defined to be a third vector C such that AxB=C, where the magnitude of C is

C =|C|=ABsinθ

and the direction of C is perpendicular to both A and B in a right-handed. θ is the smaller angle between A and B and the direction of C is found by the following rule. Extend the fingers of your right hand along with A and then curl them toward B as if you were rotating A through θ. Your thumb will then point in the direction of C. The vector product BxA has a magnitude BAsinθ but its direction, found by rotating B into A through θ, is opposite to that of C. Therefore,

BxA=-C=-(AxB) and the commutative law does not hold for the cross product

## What is Meant by Cross Product?

Vector perpendicular to two given vectors, a and b, and having a magnitude equal to the product of the magnitudes of the two given vectors multiplied by the sine of the angle between the two given vectors, usually represented by a × b.

a×b=|a| |b|sin(θ)n

► We define the cross product of two vectors in the following way...

► v x w is a vector orthogonal to both v and w consistent with the right-hand rule

► ||v x w|| is the area of the parallelogram with adjacent sides v and w

## Cross product formula ## Dot product vs Cross product 