Vector Operations Calculator
Easily perform fundamental vector operations like addition, subtraction, and the dot product for 2D and 3D vectors. Perfect for students tackling linear algebra or physics problems.
Enter the X-component of Vector A
Enter the Y-component of Vector A
Enter the Z-component of Vector A (optional, leave blank for 2D)
Enter the X-component of Vector B
Enter the Y-component of Vector B
Enter the Z-component of Vector B (optional, leave blank for 2D)
Easily perform fundamental vector operations like addition, subtraction, and the dot product for 2D and 3D vectors. Perfect for students tackling linear algebra or physics problems.
Vector Addition: A + B = (Ax + Bx, Ay + By, Az + Bz) Vector Subtraction: A - B = (Ax - Bx, Ay - By, Az - Bz) Dot Product: A · B = (Ax * Bx) + (Ay * By) + (Az * Bz)
Let's say you have Vector A with components (2, 3, 1) and Vector B with components (4, -1, 5). 1. Vector Addition (A + B): (2+4, 3+(-1), 1+5) = (6, 2, 6) 2. Vector Subtraction (A - B): (2-4, 3-(-1), 1-5) = (-2, 4, -4) 3. Dot Product (A · B): (2*4) + (3*-1) + (1*5) = 8 - 3 + 5 = 10 Our calculator will show you these results instantly.
In mathematics and physics, a vector is a quantity that has both magnitude (size) and direction. It's often represented as an arrow or as a set of components (like x, y, z coordinates) in a coordinate system.
Vector addition combines two vectors to find a resultant vector, often thought of as following one vector then the other. Vector subtraction finds the difference between two vectors, essentially adding the negative of the second vector to the first. Both operations are performed component-wise.
The dot product is an algebraic operation that takes two vectors and returns a single number (a scalar). It's calculated by multiplying corresponding components of the two vectors and then summing those products. The dot product is useful for finding the angle between two vectors or determining if they are perpendicular.
Yes! For 2D vectors, simply leave the Z-component fields blank or enter 0. The calculator will automatically treat them as zero and perform the operations in two dimensions.
Vector Operations Calculator: Add, Subtract, and Find Dot Products
© 2025-2026 PromathTools. All rights reserved.
Built by KruskalCode – SaaS & Automation Experts
