Math & Algebra Tool

Vector Calculator

Calculate Magnitude, Dot Product, and Addition for 3D vectors.

Vector A

Vector B

Σ The Formula

Magnitude: |v| = √(x²+y²+z²) | Dot Product: A·B = AxBx + AyBy + AzBz

Real World Examples

Dot Product
(1,2,3) · (4,5,6) = 32
Magnitude
|(3,4,0)| = 5
Unit Vector
v / |v| → Length becomes 1
Vector Addition
(1,2) + (3,4) = (4,6)

# About This Calculator

A Vector is a geometric object that has both magnitude (length) and direction. They are crucial in physics (for velocity, force) and computer graphics.

This tool performs operations on 3D vectors (x, y, z):
• Magnitude: The length of the vector using the distance formula.
• Dot Product: A scalar value used to find angles between vectors.
• Addition/Subtraction: Combining forces or paths.
• Unit Vector: Scaling a vector to have a length of exactly 1.

Simply enter the coordinates of your vectors to get detailed results for all these properties.

How To Use

  1. Enter x, y, z components for Vector A.
  2. Enter components for Vector B (if needed for dot product/addition).
  3. Click Calculate.
  4. View all calculated properties below.

Frequently Asked Questions

What is a Dot Product?+

It's a way to multiply two vectors to get a single number (scalar). If the dot product is 0, the vectors are perpendicular (at 90 degrees).

What is a Unit Vector?+

A vector with a length (magnitude) of 1. It is used to specify direction without magnitude. You find it by dividing a vector by its own length.

Can I use 2D vectors?+

Yes! Just enter '0' for the Z component (e.g., x=3, y=4, z=0).

What is a Cross Product?+

Unlike the dot product, the cross product results in a NEW vector perpendicular to both originals. This tool focuses on dot product and magnitude currently.

How do you add vectors?+

You add their corresponding components. (x1, y1) + (x2, y2) = (x1+x2, y1+y2). It helps find the 'resultant' force or path.

Is Vector Calculator free to use?+

Yes, Vector Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.

About

A Vector is a geometric object that has both magnitude (length) and direction. They are crucial in physics (for velocity, force) and computer graphics.

This tool performs operations on 3D vectors (x, y, z):
• Magnitude: The length of the vector using the distance formula.
• Dot Product: A scalar value used to find angles between vectors.
• Addition/Subtraction: Combining forces or paths.
• Unit Vector: Scaling a vector to have a length of exactly 1.

Simply enter the coordinates of your vectors to get detailed results for all these properties.

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