Dot Product Calculator

This Dot Product Calculator helps you find the dot product of two 3D vectors. Multiply the corresponding components, then add those products together to get the final scalar value. This follows the dot 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 dot product formula A · B = a₁b₁ + a₂b₂ + a₃b₃.
3. Substitute values, multiply, and add.

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 dot product formula.

In this problem: Use A · B = a₁b₁ + a₂b₂ + a₃b₃.

Step 3a - Substitute the values.

In this problem: Replace aᵢ and bᵢ with your values.

Step 3b - Multiply.

In this problem: Multiply each pair of components.

Step 3c - Add (and simplify if needed).

In this problem: Add the products to get the dot product.

Final answer: A · B = 32

Example 2: (1/2,0,0),(2,3,4)

Step 1 - Identify the components.

In this problem: From the given vectors A = (1/2, 0, 0) and B = (2, 3, 4), the components are:

Step 2 - Write the dot product formula.

In this problem: Use A · B = a₁b₁ + a₂b₂ + a₃b₃.

Step 3a - Substitute the values.

In this problem: Replace aᵢ and bᵢ with your values.

Step 3b - Multiply.

In this problem: Multiply each pair of components.

Step 3c - Add (and simplify if needed).

In this problem: Add the products to get the dot product.

Final answer: A · B = 1