Magnitude of a Vector Calculator

This Magnitude of a Vector Calculator helps you find the length of a 3D vector. Square each component of the vector, add the results, and then take the square root to get the final value. This follows the magnitude 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. Write the magnitude formula.
3. Substitute and compute inside the square root.
4. Simplify the square root (if possible).

Formula:

Example 1: (3,4,0)

Step 1 - Identify the components.

In this problem: Write the component values.

Step 2 - Write the formula.

In this problem: Use the magnitude formula.

Step 3a - Substitute values.

In this problem: Replace a₁, a₂, a₃ with your values.

Step 3b - Solve the squares.

In this problem: Evaluate each squared term.

Step 3c - Add the terms.

In this problem: Add inside the square root.

Step 4 - Simplify.

In this problem: No further simplification is needed.

Final answer: |A| = 5

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

Step 1 - Identify the components.

In this problem: Write the component values.

Step 2 - Write the formula.

In this problem: Use the magnitude formula.

Step 3a - Substitute values.

In this problem: Replace a₁, a₂, a₃ with your values.

Step 3b - Solve the squares.

In this problem: Evaluate each squared term.

Step 3c - Add the terms.

In this problem: Add inside the square root.

Step 4 - Simplify.

In this problem: No further simplification is needed.

Final answer: |A| = 1/2