i            j          k






(u2 x v3) – (v2 x u3) i = () i

(v1 x u3) – (u1 x v3) j = () j

(u1 x v2) – (v1 x u2) k = () k


Answer: i + j + k


About Cross Product & Cross Product Calculator




cross product calculator
Fig. 1

A vector has two parts. One part is its magnitude and the second one is its direction. We can take two types of products of vectors. One is called scalar product or dot product and the other is called vector product or cross product. Cross product calculator performs a binary operation on three-dimensional space. Cross product calculator gives the resultant vector.

The direction of resultant vector in cross product can be found using right-hand rule as shown in figure (1).


Cross product has many applications in practical life. It is used in engineering, physics and computer programming. It is completely different from scalar product. It does not follow commutative law which means AxB is not equal to -(AxB). It follows the rules that are:

  • i x j = k
  • j x k = i
  • k x i = j
  • j x i = -k
  • k x j = -i
  • i x k = -j

According to definition of cross product, i x i = j x j = k x k = 0.

Some of the applications are Torque, Angular Momentum, Rigid Body, Lorentz Force.

Our cross product calculator will provide you resultant vector. Cross product calculator will also show you the steps performed during calculation. Hence, cross product calculator will not only gives you a correct answer, but also teaches you the way to solve a cross product manually.

This cross product calculator is Javascript based. It performs calculations in front of you.

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