Vector Calculator

What Is a Vector Calculator?

A vector calculator performs common vector operations in 2D or 3D space. Enter two vectors and choose addition, subtraction, dot product, cross product, projection, normalization, or the vector between two points.

Vector Operations

Addition and subtraction are done component-wise. The dot product returns a scalar:

$$\mathbf{a} \cdot \mathbf{b} = a_x b_x + a_y b_y + a_z b_z$$

The cross product (3D only) produces a vector perpendicular to both inputs:

$$\mathbf{a} \times \mathbf{b} = (a_y b_z - a_z b_y,\ a_z b_x - a_x b_z,\ a_x b_y - a_y b_x)$$

Frequently Asked Questions

How do I add two vectors?

Add each matching component: if a = (2, 3) and b = (1, -2), then a + b = (3, 1).

What is the dot product used for?

The dot product measures how aligned two vectors are. It equals |a||b|cos(θ) and is widely used in physics and graphics.

Can I compute cross product in 2D?

No. The cross product is defined for 3D vectors. Switch to 3D mode to use this operation.

How do I find the vector between two points?

Subtract the start point from the end point: b - a gives the displacement vector from a to b.

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What Is a Vector Calculator?

Vector Operations

Frequently Asked Questions

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