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
- 01
Enter the two vectors
Input vectors in component form, e.g., a = (1, 2, 3) and b = (4, 5, 6).
- 02
Compute determinants
Calculate the determinant of a 3x3 matrix formed with unit vectors and vector components.
- 03
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.
Related Topics
More step-by-step guides in Mathematics and adjacent subjects.
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