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

Cross product formula

Dot product vs Cross product

Dot product vs Cross product