Vector Calculator

Perform Vector Operations

Use this calculator to perform various operations on 3D vectors.

Vector A

Vector B

How to Use the Vector Calculator

Our Vector Calculator is a powerful tool designed to perform various operations on 3D vectors. Here's a comprehensive guide on how to use it:

Vector Operations

The calculator supports the following operations:

  • Dot product (a · b)
  • Cross product (a × b)
  • Addition (a + b)
  • Subtraction (a - b)
  • Angle between vectors
  • Vector projection
  • Magnitude calculation
  • Vector normalization

How to Perform Calculations

  1. Select the desired operation from the dropdown menu.
  2. Enter the components of Vector A (x, y, z).
  3. For operations involving two vectors, enter the components of Vector B.
  4. Click the "Calculate" button to see the result.

Example Calculation: Dot Product

Let's calculate the dot product of vectors a = (3, 4, 2) and b = (1, -2, 5):

  1. Select "Dot product a · b" from the operation dropdown.
  2. Enter Vector A: x = 3, y = 4, z = 2
  3. Enter Vector B: x = 1, y = -2, z = 5
  4. Click "Calculate"

The calculator will show:

  • Result: 13
  • Steps: a · b = (3 × 1) + (4 × -2) + (2 × 5) = 3 - 8 + 10 = 13

Visual Representation

For operations like vector addition or cross product, the calculator provides a visual diagram to help you understand the spatial relationship between the vectors.

X Y Z Vector A (3,4,2) Vector B (1,-2,5) Result Vector A: |A| = 5.39 Vector B: |B| = 5.48 Result: Varies by operation type Grid: 1 unit = 50px

This diagram illustrates an example of vector addition, showing Vector A (blue), Vector B (green), and their sum (red).

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