Vector Math

Cross Product Calculator

Generate the vector orthogonal to two 3D inputs and inspect its magnitude.

cross productvector productorthogonal vector
Cross Product (3D)

Compute the vector orthogonal to both inputs in ℝ³.

Note: Enter x, y, z components separately

A × B
(8.00, -13.00, 6.00)
‖A × B‖
16.401219

Cross product (ℝ³)

A × B = (a₂b₃ − a₃b₂, a₃b₁ − a₁b₃, a₁b₂ − a₂b₁)

The resulting vector is perpendicular to both inputs, making it useful for torque and area calculations.

How to use

  1. Enter two 3-component vectors.
  2. Confirm the components correspond to x, y, and z values.
  3. Review the cross product vector and its magnitude.

Example

Input: A = (1, 2, 3), B = (−3, 0, 4)

Output: A × B = (8, −13, 6), ‖A × B‖ ≈ 16.5529

Student-friendly breakdown

This walkthrough emphasizes the most searched ideas for Cross Product Calculator: vector calculator, vector addition calculator, dot product calculator, cross product calculator. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.

Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic. Each resource is interlinked so crawlers (and readers) can discover the next best action within a couple of clicks—one of the easiest ways to lift topical authority.

Deep dive & study plan

The Cross Product Calculator is a go-to tool whenever you need to computes the vector cross product in three dimensions.. It focuses on cross product, vector product, orthogonal vector, which means searchers often arrive with intent-heavy queries like “how to cross product calculator quickly” or “cross product calculator formula explained.” Use this calculator to capture those intents and keep learners on the page long enough to send positive engagement signals.

Under the hood, the calculator leans on the resulting vector is perpendicular to both inputs, making it useful for torque and area calculations.—that’s why we surface the full expression (“A × B = (a₂b₃ − a₃b₂, a₃b₁ − a₁b₃, a₁b₂ − a₂b₁)”) directly above the interactive widget. When you embed that formula inside H2s or supporting paragraphs, you help both humans and crawlers understand what entity the page represents.

Execution matters as much as the math. Follow the built-in procedure: Step 1: Enter two 3-component vectors. Step 2: Confirm the components correspond to x, y, and z values. Step 3: Review the cross product vector and its magnitude.. Each numbered instruction is short enough to scan on mobile but descriptive enough to satisfy Google’s Helpful Content guidelines. Encourage students to jot down units, double-check signs, and compare answers with the Example card to build confidence.

The Example section itself is packed with semantic clues: “A = (1, 2, 3), B = (−3, 0, 4)” leading to “A × B = (8, −13, 6), ‖A × B‖ ≈ 16.5529.” Pepper similar narratives throughout your copy (and internal links from related guides) so canonical search intents are answered without pogo-sticking back to Google.

Quick retention checklist

  • Speak the formula aloud (or annotate it) so the relationships stick.
  • Write each step in your own words and compare with the numbered list above.
  • Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
  • Link out to at least two related calculators to keep readers exploring your topical hub.

FAQ & notes

Can I use this for 2D vectors?

The cross product in this calculator is defined for 3D vectors. Extend 2D vectors by adding a zero z-component if needed.

What if my vectors are parallel?

Parallel vectors produce a zero vector because they have no perpendicular component.

What formula does the Cross Product Calculator use?

The resulting vector is perpendicular to both inputs, making it useful for torque and area calculations.

How do I use the Cross Product Calculator?

Enter two 3-component vectors. Confirm the components correspond to x, y, and z values. Review the cross product vector and its magnitude.