Vector Calculator
🎯 Vector A
🎯 Vector B
Vector Calculator
Perform all essential vector operations: addition, subtraction, dot product, cross product, magnitude calculation, and unit vector computation.
Basic Vector Operations:
- Vector Addition: (a₁, a₂, a₃) + (b₁, b₂, b₃) = (a₁+b₁, a₂+b₂, a₃+b₃)
- Vector Subtraction: (a₁, a₂, a₃) - (b₁, b₂, b₃) = (a₁-b₁, a₂-b₂, a₃-b₃)
- Dot Product: a⃗ · b⃗ = a₁b₁ + a₂b₂ + a₃b₃
- Cross Product: a⃗ × b⃗ = (a₂b₃-a₃b₂, a₃b₁-a₁b₃, a₁b₂-a₂b₁)
- Vector Magnitude: |a⃗| = √(a₁² + a₂² + a₃²)
Applications:
- Physics: Force, velocity, acceleration calculations
- Engineering: Structural analysis, mechanics
- Computer Graphics: 3D transformations, lighting
- Navigation: Direction and distance calculations
How to Use:
Enter the coordinates of vectors A and B, select an operation, and get detailed results with step-by-step calculations.
Frequently Asked Questions
What is a dot product of vectors?
The dot product is a scalar value equal to the sum of products of corresponding coordinates. It measures how much vectors point in the same direction.
How is cross product different from dot product?
Dot product gives a scalar (number), while cross product gives a vector perpendicular to both original vectors.
How to find a unit vector?
A unit vector is obtained by dividing a vector by its magnitude: û = a⃗/|a⃗|. It has the same direction but length 1.
What does vector magnitude represent?
Vector magnitude (or length) is the distance from origin to the vector's endpoint, calculated using the Pythagorean theorem.
When is the cross product zero?
Cross product is zero when vectors are parallel (pointing in the same or opposite directions).