Cross Product Calculator

This Cross Product Calculator helps you find the cross product of two 3D vectors. Calculate each component using the cross product rule, then combine the results to form the final vector. This follows the cross product formula used in coordinate geometry and vector algebra. It is a simple way to check answers, understand the method clearly, and practise vector operations step by step.

Step-by-step method

1. Identify the vector components.
2. Use the cross product component formula.
3. Substitute values and simplify.

Formula:

Example 1: (1,2,3),(4,5,6)

Step 1 - Identify the components.

In this problem: From the given vectors A = (1, 2, 3) and B = (4, 5, 6), the components are:

Step 2 - Write the cross product formula.

In this problem: Use the component formula for A × B.

Step 3a - Substitute values.

In this problem: Substitute the components into the cross product formula.

Step 3b - Multiply the pairs.

In this problem: Compute each product in the components.

Step 3c - Simplify the components.

In this problem: Subtract to get the final components.

Final answer: A×B = (-3, 6, -3)

Example 2: (1/2,0,0),(2,0,0)

Step 1 - Identify the components.

In this problem: From the given vectors A = (1/2, 0, 0) and B = (2, 0, 0), the components are:

Step 2 - Write the cross product formula.

In this problem: Use the component formula for A × B.

Step 3a - Substitute values.

In this problem: Substitute the components into the cross product formula.

Step 3b - Multiply the pairs.

In this problem: Compute each product in the components.

Step 3c - Simplify the components.

In this problem: Subtract to get the final components.

Final answer: A×B = (0, 0, 0)