Use this interactive vector explorer to learn vectors in 1D, 2D, and 3D. Change vector components, insert a second vector, and watch graphs, formulas, magnitudes, directions, and step-by-step solutions update instantly.
How to use the interactive vector explorer
Choose 1D, 2D, or 3D
Start in 2D for the clearest graph, then try 1D and 3D when you are ready.
Enter Vector A
Change the x, y, and z components to see the vector move on the graph.
Insert Vector B
Add a second vector to unlock addition, subtraction, dot product, cross product, and angle calculations.
Read the worked steps
Use the formulas and step-by-step panel to understand how the final answer is calculated.
Core idea
A vector has both size and direction. Components tell how far the vector moves along each axis. By combining components, students can find magnitude, direction, sums, differences, products, and unit vectors.
Useful vector formulas
Magnitude
|A| = √(Ax2 + Ay2)Magnitude is the length of the vector.
Vector addition
A + B = (Ax + Bx, Ay + By)Add matching components to combine vectors.
Dot product
A · B = |A||B|cosθThe dot product helps find the angle between two vectors.
Unit vector
 = A / |A|A unit vector points in the same direction but has length 1.
Ideas for practice
- Use A = <3, 4> and check that the magnitude is 5.
- Insert B = <2, -1> and calculate A + B.
- Switch to angle mode and compare degrees with radians.
- Try 3D mode and explore the cross product.
Frequently asked questions
What is a vector?
A vector is a quantity with magnitude and direction, such as displacement, velocity, force, or acceleration.
What are vector components?
Components are the parts of a vector along each axis, such as x, y, and z.
What does the dot product show?
The dot product helps compare how much two vectors point in the same direction. It is also used to find the angle between vectors.
What is a unit vector?
A unit vector has length 1 and shows direction only.
