All standard operations.
Add, scale, dot, cross, magnitude, normalize, angle, project, orthogonalize.
Complete
EN
Vector Solver
Vector operations, computed step by step.
Type or photograph the vectors. AskSia handles addition, scalar multiplication, dot product, cross product, magnitude, normalization, angle between vectors, projection, and orthogonalization, with each step shown.
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
4.9 / 5 · trusted by 2M+ students · 50M+ problems solved
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 vector operations does AskSia handle?
The vector solver handles all standard operations: addition (component-wise), scalar multiplication, dot product, cross product (3D only), magnitude (square root of sum of squares), normalization (divide by magnitude), angle between two vectors (arccosine of dot product over product of magnitudes), projection of one vector onto another, and Gram-Schmidt orthogonalization of a set of vectors. 2D, 3D, and higher dimensions all supported, though cross product is only in 3D.
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia for Vector.
Every step transparent, every answer self-checked.
2D, 3D, higher.
Operations generalize across dimensions, except cross product (3D only).
Dimension-aware
Angle computation.
Arccosine of the dot product over the product of magnitudes.
Geometry
Projection and rejection.
Projection of u onto v with the standard formula. Rejection is u minus the projection.
Geometric
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 Vector 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
Hi! What are we studying today?
Ask about your homework, lecture, or readings...↑
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
☰
AskSia
+What can I do for you?
Homework solver
Live transcribe
File summary
Snap
YouTube
Flashcard
Calc
98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What the Vector solver covers.
Vector addition.
Component-wise. AskSia shows each component addition.
Addition
Dot product.
Sum of products of corresponding components. Reveals angle and projection.
Dot
Cross product (3D).
Determinant formula. Gives perpendicular vector with parallelogram area.
Cross
Angle between vectors.
Arccosine of dot product divided by product of magnitudes.
Angle
Projection.
Project u onto v with the standard formula. Useful for decomposing vectors.
Project
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 do you compute the magnitude of a vector?
The magnitude of a vector is the square root of the sum of the squares of its components. This is the Euclidean distance from the origin to the vector's tip. For 2D and 3D, this is the standard distance formula. AskSia computes the magnitude with exact symbolic arithmetic when possible (radicals) and a decimal approximation.
What does the dot product tell you?
The dot product u dot v equals the magnitudes of u and v times the cosine of the angle between them. It is zero exactly when the vectors are perpendicular (orthogonal). Positive dot product means the vectors point in similar directions (angle less than 90 degrees); negative means opposite directions. It also gives the scalar projection of u onto the direction of v.
Why is the cross product only defined in 3D?
The cross product produces a vector perpendicular to two given vectors, and in 3D, the perpendicular direction is essentially unique (up to sign), making the cross product well-defined. In 2D, two vectors do not generally have a perpendicular within 2D. In higher dimensions, the perpendicular space is more than 1D, so there is no single 'cross product' vector.
How do you project one vector onto another?
The projection of u onto v is given by the formula: scalar coefficient (u dot v over v dot v) times v. The scalar coefficient is the signed length of the shadow of u along v, and multiplying by v scales the projection to the right magnitude in the direction of v. AskSia computes both the scalar projection and the full projection vector.
How accurate is AskSia?
AskSia hits 98% accuracy on standard high school and college coursework, measurably higher than ChatGPT, Photomath, and Symbolab on the same problem sets. 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.
Start Today
Add, scale, dot, cross, project.
Join 2M+ students using AskSia to solve vector problems step-by-step. Photo input, plain-English explanations, and a verification check on every solve.