Example Data Table
| Item | Value | Meaning |
|---|---|---|
| Vector A | (3, 4, 0) | Right and upward movement. |
| Vector B | (-2, 5, 1) | Left, upward, and forward movement. |
| Scribble path | 0,0,0; 3,4,0; 5,1,1; 7,2,0 | Connected points from a rough drawing. |
| Scalar | 2 | Value used to stretch vector A. |
Formula Used
Magnitude: |A| = √(Ax² + Ay² + Az²)
Addition: A + B = (Ax + Bx, Ay + By, Az + Bz)
Subtraction: A - B = (Ax - Bx, Ay - By, Az - Bz)
Dot product: A · B = AxBx + AyBy + AzBz
Cross product: A × B = (AyBz - AzBy, AzBx - AxBz, AxBy - AyBx)
Angle: θ = cos⁻¹((A · B) / (|A||B|))
Projection: projB(A) = ((A · B) / |B|²)B
Scribble path length: Sum of distances between consecutive points.
How to Use This Calculator
Select a calculation type. Choose Cartesian or magnitude angle input for each vector. Enter components, angles, units, and scalar value. Add scribble points in order. Use commas inside each point. Separate points with semicolons or new lines. Press calculate to see the result below the header. Use CSV or PDF export when you need a saved copy.
Vector Scribbles for Clear Work
A vector scribble is a fast visual note. It shows direction, size, and movement. This calculator turns those notes into numbers. It accepts coordinate form and polar form. It also accepts a small path of points. That makes it useful for classroom work, field sketches, and quick checks.
Why Vectors Need Structure
Vectors are more than arrows. Each arrow has components. Each component belongs to an axis. When the components are known, many operations become simple. Addition combines matching axes. Subtraction compares matching axes. Dot products measure alignment. Cross products measure turning effect. Unit vectors show direction without size. Projection shows how much one vector follows another.
Using Scribble Points
The scribble field stores points in order. Each point can use x,y or x,y,z form. The calculator measures every small segment. It then reports total path length. It also reports net displacement. This helps when a drawn route is not straight. A long route can still end with a short displacement.
Practical Uses
Use the tool for geometry, motion, maps, and simple graphics planning. A designer can test arrow directions. A student can compare two forces. A teacher can build examples for vector addition. A technician can estimate movement from marked points. The values are rounded for reading, but the calculations use decimal inputs.
Result Exports
CSV export is useful for spreadsheets. It keeps labels and values in rows. The PDF export is useful for saving a clean record. Both options use the same inputs. First calculate the result. Then choose the format that fits your report.
Good Input Habits
Keep units consistent. Do not mix meters and feet. Use degrees for angle fields. Enter elevation only when three dimensional direction matters. For a flat vector, leave elevation at zero. Check signs on coordinates. Negative x and y values change direction. Small notes in the scribble box can guide your review. Clear input gives clear vector answers.
Reading the Output
Read the summary before the details. The selected operation appears first. Component tables follow. Angle values use degrees. Magnitudes stay positive. Cross product signs show orientation. Projection values describe shadow length. Use the example table to compare expected patterns before changing values.
FAQs
What is a vector scribble?
It is a rough path or arrow sketch written as ordered points. The calculator converts those points into measurable path length, displacement, and centroid values.
Can I use two dimensional vectors?
Yes. Enter x and y values, then keep z at zero. The calculator still shows a full component report for consistent output.
Can I enter polar style values?
Yes. Choose magnitude and angles for a vector. The page converts magnitude, angle, and elevation into x, y, and z components.
What does the dot product show?
The dot product shows alignment. A positive value suggests similar direction. A negative value suggests opposite direction. Zero suggests perpendicular direction.
What does the cross product show?
The cross product creates a vector perpendicular to both input vectors. Its magnitude relates to the area formed by the two vectors.
How should scribble points be typed?
Type points as x,y or x,y,z. Separate each point with a semicolon or a new line. Keep the order from your sketch.
Why is my angle unavailable?
The angle calculation needs two nonzero vectors. If either vector has zero magnitude, the direction is undefined.
Do exports use the current inputs?
Yes. The CSV and PDF buttons calculate with the current form values, then download the matching result summary and detail rows.