Cross Product Calculator of Vectors

cross product diagram

cross product formula

 i     j     k
 i     j     k


This Cross Product calculates the cross product of 2 vectors based on the length of the vectors' dimensions.

This calculator can be used for 2D vectors or 3D vectors. If a user is using this vector calculator for 2D vectors, which are vectors with only two dimensions, then s/he only fills in the i and j fields and leave the third field, k, blank. If using this calculator for a 3D vector, then the user enters in all fields.

The cross product of the two vectors which are entered are calculated according to the formula shown above. The i, j, and k fields are multiplied together and added up to give the total resultant.

The resultant of a cross product is a vector value. Unlike dot product which produces a scalar value (the length of the 2 vectors added up), the cross product produces a vector, so it has value and direction.

The cross product vector is a very important calculation in engineering because many vector values are computed by cross product. Examples include torque and magnetic force. Torque, such as that experienced in the rotation of electric motors, is the vector product of radius vector and applied force. Magnetic force is the vector product of a charge and the velocity of the charge. Both of these products, torque and magnetic force, create new vectors based on their 2 vector constituents. Cross product is just a calculation that creates a new vector based on the 2 vectors which cross in calculation. The direction that the newly created 3rd vector faces is perpendicular to both of the 2 constituent vectors.

Example Calculations
Calculate the cross product of the following 2 vectors:
A= 7i + 3j + 9k
B= 3i - 4j + 7k


Cross Product A x B= [(3*7) - (9*-4)]i + [(9*3) - (7*7)]j + [(7*-4) - (3*3)]k= 57i -22j -37k

Calculate the cross product of the following 2 vectors:
A= 2i + 5j - 6k
B= 3i + 2j + 8k


Cross Product A x B= [(5*8) - (-6*2)]i + [(-6*3) - (2*8)]j + [(2*2) - (5*3)]k= 52i -34j -11k

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