Vector Calculator | 3D Vector Operations

Free online calculator for vector operations with step-by-step solutions

Vector Operations

First Vector:

Operation:

Second Vector:

Vector Operations Guide

Basic Operations

Understanding vector operations:

Dot Product:
Scalar result: a·b = ax×bx + ay×by + az×bz
Cross Product:
Vector perpendicular to both input vectors
Magnitude:
Length of vector: |a| = √(ax² + ay² + az²)

Advanced Operations

Additional vector calculations:

Unit Vector:
Vector with magnitude 1: û = u/|u|
Vector Angle:
θ = arccos(a·b / |a||b|)
Projection:
proj_b(a) = (a·b̂)b̂