Enter Five Vectors
Example Data Table
| Vector | X | Y | Z |
|---|---|---|---|
| A | 2 | 1 | 3 |
| B | -1 | 4 | 0 |
| C | 3 | -2 | 1 |
| D | 0 | 1 | 5 |
| E | 4 | 0 | -2 |
| Resultant | 8 | 4 | 7 |
Formula Used
Resultant vector:
R = A + B + C + D + E
Magnitude of any vector V:
|V| = √(x² + y² + z²)
Average vector:
Average = R / 5
Scalar multiplication:
S = kR
Dot product:
A · B = AxBx + AyBy + AzBz
Cross product:
A × B = (AyBz − AzBy, AzBx − AxBz, AxBy − AyBx)
Unit vector of R:
u = R / |R|
Direction angles of R:
α = cos⁻¹(Rx / |R|), β = cos⁻¹(Ry / |R|), γ = cos⁻¹(Rz / |R|)
How to Use This Calculator
- Enter the x, y, and z components for vectors A to E.
- Add a scalar value if you want a multiplied resultant.
- Press the calculate button.
- Read the resultant vector above the form.
- Review magnitudes, dot products, cross products, and direction angles.
- Download the result as CSV or PDF if needed.
About This 5 Vector Calculator
A 5 vector calculator helps you combine five different vectors in one place. It is useful in maths, mechanics, graphics, and physics. Many problems involve several forces or directions at once. Manual work can be slow. This page speeds up the process. You can enter five full three dimensional vectors and solve them together. The tool returns the resultant vector immediately. It also gives magnitudes for each vector. That helps you compare size and direction clearly.
Why the Resultant Matters
The resultant vector shows the single vector that represents the total effect of all five inputs. This is important in vector addition problems. It is also useful when combining displacement, velocity, momentum, or force. The average vector is included too. That makes pattern analysis easier. A scalar multiplier is also available. It lets you stretch or shrink the final vector without changing its direction. This is helpful in many classroom examples and practice sets.
Useful Outputs for Study and Practice
This 5 vector calculator does more than simple addition. It also shows dot products for selected vector pairs. Dot products help measure directional similarity. The cross products reveal perpendicular behavior in three dimensions. Angle outputs help you understand separation between vectors. The unit vector explains pure direction. Direction angles show how the resultant sits relative to the x, y, and z axes. These are common topics in vector algebra and analytical geometry.
Clean Workflow for Repeated Problems
The layout is simple and practical. Enter the components. Press calculate. Review the result above the form. Then export the data when you want a saved record. The sample table, formulas, and FAQs make the page easier to learn from. This is useful for homework, revision, and fast checking. If your resultant becomes zero, some direction values are undefined. That is mathematically correct. Overall, the page gives a clear path for solving five vector problems with fewer steps.
FAQs
1. What does this 5 vector calculator solve?
It combines five 3D vectors and returns the resultant vector, average vector, scaled resultant, magnitudes, dot products, cross products, unit vector, and direction angles.
2. Can I use negative vector components?
Yes. Negative values are valid. They often represent direction changes along the x, y, or z axis.
3. Why are some angles shown as undefined?
Angles become undefined when one compared vector has zero magnitude. A zero vector has no fixed direction, so the angle cannot be determined.
4. What happens if the resultant vector is zero?
The calculator still shows the resultant correctly. However, the unit vector and direction angles of that resultant are undefined.
5. What is the purpose of the scalar input?
The scalar multiplies the resultant vector after addition. It helps you study scaling effects without editing each original vector separately.
6. Why are dot and cross products included?
They provide deeper analysis. Dot products measure directional alignment. Cross products show a perpendicular vector and help in geometry and physics problems.
7. Can I download my results?
Yes. After calculation, you can export the result as a CSV file or a simple PDF file.
8. Is this calculator useful for students?
Yes. It is useful for homework, checking manual answers, revision work, and quick practice with vector algebra concepts.