Determinant formula.
Expand the (i, j, k) determinant with u and v components in rows 2 and 3.
Direct
AI Solver by AskSia
Cross Product Solver: any two 3D vectors
Type or photograph two 3D vectors. AskSia computes their cross product using the determinant formula, with the resulting components labeled. Magnitude, direction, and applications shown.
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
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asksia.ai/solver
98% · Verified
Problem
Find the area enclosed between y = x² and y = 2x in the first quadrant.
1
Find the points of intersection
Set the curves equal: x² = 2x → x(x - 2) = 0, so x = 0 and x = 2.
2
Identify which curve is on top
On (0, 2), 2x > x², so y = 2x is the upper curve.
3
Set up the area integral
A = ∫₀² (2x - x²) dx
4
Integrate term-by-term
A = [ x² - x³/3 ]₀²
Final Answer
A = 4/3 sq. units
Quick Answer
What is the cross product?
The cross product of two 3D vectors u and v is a third 3D vector u cross v that is perpendicular to both u and v. Its direction follows the right-hand rule, and its magnitude equals the magnitudes of u and v times sin of the angle between them. To compute it, expand the determinant of the matrix whose first row is the unit vectors i, j, k and second and third rows are the components of u and v. The cross product is useful for finding normal vectors to planes, computing torques, and computing areas of parallelograms.
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia for Cross Product.
Every step transparent, every answer self-checked.
Perpendicular result.
u cross v is perpendicular to both u and v, by construction.
Geometry
Magnitude meaning.
The magnitude of u cross v equals the area of the parallelogram formed by u and v.
Area
Right-hand rule.
Direction follows the right-hand rule: curl fingers from u to v, thumb points along the cross product.
Direction
Photo, paste, or type.
Snap handwritten or printed problems with your phone, paste from any online homework portal, or type with full LaTeX support.
Multi-modal input
Verified by AskSia.
Every answer gets a self-check pass. Sia catches sign errors and algebra mistakes before you submit your homework.
Self-checked
How It Works
Solve any Cross Product problem in three steps.
Step 01
Enter the problem.
Type the expression, paste from your homework, snap a photo, or speak it. AskSia parses your input and identifies the structure.
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
AskSia picks the method.
Based on the problem structure, AskSia chooses the cleanest solution path and labels each step with the operation performed.
1
Set curves equal
x² = 2x → x = 0, x = 2
2
Set up the integral
A = ∫₀² (2x - x²) dx
3
Evaluate
A = [x² - x³/3]₀² = 4/3
Step 03
Read the verified answer.
Final result appears with a substitution or composition check. Practice problems on the same concept are one tap away.
Auto-generated diagram
Region between y = 2x and y = x² — area = 4/3
Available On
Solve anywhere
you study.
Every solve syncs across Web, iOS, and Android — start it at your desk, finish on your phone.
Web App
Full study studio
Split-panel interface with the worked solution on the left, the auto-generated diagram and AI tutor chat on the right.
Drag & drop image upload + LaTeX equation editor
Auto-generated diagrams render alongside steps
Side-panel AI tutor chat for hints and alt methods
Export to PDF, DOCX, Notion, or Google Docs
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Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
Mobile App
Snap & solve, anywhere
Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.
One-tap snap-and-solve on iOS and Android
Pinch-to-zoom diagrams, swipe between steps
Auto-sync solves with your Web library
Offline review of saved solutions and flashcards
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1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What the Cross Product solver covers.
Standard 3D vectors.
Compute the cross product using the determinant formula.
Standard
Normal to a plane.
Two vectors in the plane have a cross product perpendicular to the plane.
Plane
Area of parallelogram.
The magnitude of u cross v is the area of the parallelogram spanned by u and v.
Area
Torque in physics.
Torque equals r cross F, where r is position vector and F is force.
Physics
Triangle area.
Half of the magnitude of AB cross AC gives the area of triangle ABC.
Triangle
Verify your homework.
Paste your candidate answer and the original problem. AskSia walks the work, flags any divergent step, and tells you the correct final value.
Answer check
Compare
AskSia vs. ChatGPT,
Photomath & Symbolab.
General chatbots hallucinate. Photo solvers stop at math. AskSia is built for actual coursework with verified accuracy, visual learning, and every subject.
| Feature | AskSia Solver | ChatGPT | Photo Solvers |
|---|---|---|---|
| Solution accuracy | ✓ 98% | ~70-85%, hallucinations | ~90%, math only |
| Auto-generated diagrams | ✓ Every solve | Inconsistent / broken | Graphs only, math-only |
| Step-by-step explanations | ✓ Numbered + plain English | Inconsistent depth | ✓ Math steps |
| Subject coverage | ✓ Math, Physics, Chem, Bio, CS, Econ | ✓ Wide but unverified | Math only |
| Photo input | ✓ Handwriting + diagrams + code | Photos OK, weak on handwriting | ✓ Math photos only |
| Answer verification | ✓ Self-checked before display | No verification | Math engine only |
| Tutor follow-ups | ✓ Hints, alt methods, ELI5 | ✓ General chat | Not available |
| Practice and flashcards | ✓ One-tap from any solve | Manual prompting | Not available |
| Code debugging | ✓ Python, Java, C++, SQL... | ✓ Yes | Not available |
| Free to start | ✓ Daily solves, no card | Limited model access | Steps locked behind paywall |
FAQ
Frequently asked questions.
How is the cross product different from the dot product?
The dot product of two vectors is a scalar, while the cross product is a vector. The dot product measures alignment, while the cross product measures perpendicularity. The cross product only exists in 3D (and 7D), while the dot product works in any dimension.
How does the right-hand rule work?
Point your right hand's fingers in the direction of u, curl them toward v in the shorter angular direction. Your thumb points in the direction of u cross v. So the cross product is perpendicular to both u and v, pointing out of the u-v plane in the orientation given by the right-hand rule.
Is the cross product commutative?
No. The cross product is anti-commutative: u cross v equals negative of v cross u. Swapping the order reverses the direction. The magnitude is the same, but the sign of each component flips. This is why the order matters for finding the correct direction.
How do you compute the cross product?
Use the determinant formula. The cross product is computed as the determinant of a 3x3 matrix whose first row is the unit vectors i, j, k, second row is the components of u, and third row is the components of v. Expand along the first row to get the three component formulas. AskSia performs this expansion explicitly.
How accurate is AskSia?
AskSia is engineered for accuracy on standard high school and college coursework. Accuracy comes from subject-specialized models, a symbolic verification pass that catches arithmetic errors, and a self-check step that re-derives the answer before showing it to you.
Can I get practice problems and flashcards?
Yes. After any solve, ask Sia to generate similar practice problems at SAT, ACT, AP, IB, or college difficulty, or build a flashcard set on the underlying concept in one tap. Useful for exam prep and spaced repetition before a quiz, midterm, or final.
How much does AskSia cost?
AskSia has a free plan that includes daily solves across all subjects. AskSia Pro and Super include unlimited solves, advanced subjects, the full AI tutor companion, exports, and priority response speed. See pricing for details.
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