Mathematics
The Cross Product
The cross product of two vectors, denoted by a × b, results in a third vector perpendicular to the plane containing a and b. It is used in physics for torque and rotational calculations. ScanSolve helps find the cross product and explains each step with diagrams.
How to Approach The Cross Product
Enter the two vectors
Input vectors in component form, e.g., a = (1, 2, 3) and b = (4, 5, 6).
Compute determinants
Calculate the determinant of a 3x3 matrix formed with unit vectors and vector components.
Verify perpendicularity
Check that the resulting vector is orthogonal to the original vectors.
Frequently Asked Questions
What is the result of a cross product?+
The result is a vector perpendicular to the original two vectors, representing area and direction.
When is the cross product zero?+
The cross product is zero when the vectors are parallel or one is a zero vector.
How to determine the direction of the cross product vector?+
Use the right-hand rule: Point your index along a and middle finger along b; your thumb shows the result's direction.
Stuck on a The Cross Product problem?
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