Vector Addition & Resolution Playground Physics

Resultant: ---

Drag vector tips to change magnitude and direction. Click near a tip to select, then drag. Resultant updates in real time.

What is the Vector Addition Playground?

Quick Answer: An interactive tool to visually add and resolve 2D vectors. Drag arrow tips to set magnitude and direction; the resultant vector (sum) is computed and displayed live, along with component breakdown, magnitude, and angle. Perfect for physics and linear algebra basics.

Theory of Vector Addition

Vectors are quantities with both magnitude and direction. In a Cartesian plane, any vector A can be expressed as (Ax, Ay). The resultant of several vectors is their component-wise sum: Rx = Σ Ax, Ry = Σ Ay. Magnitude |R| = √(Rx2 + Ry2) and direction θ = tan-1(Ry/Rx). This playground lets you freely drag vectors and instantly see how the resultant changes.

Step-by-Step Examples

Example 1: Adding Perpendicular Vectors

  1. Click "Add Vector" twice. Drag one to point right (e.g., (4,0)), the other straight up (0,3).
  2. The resultant has components (4,3), magnitude 5, angle ~36.87°. The info panel shows this.

Example 2: Zero Resultant (Equilibrium)

  1. Add three vectors. Drag them to form a closed triangle: e.g., (2,0), (-1, 1.732), (-1, -1.732).
  2. If they cancel perfectly, the resultant becomes zero (magnitude 0).

Example 3: Resolving a Single Vector

  1. Clear all, then add one vector. Drag it to any angle. Observe its x and y components displayed in the table.
  2. The angle is measured from the positive x-axis.

Frequently Asked Questions

How do I add more vectors?

Click the "+ Add Vector" button. A new arrow appears at a default position; you can then drag its tip.

Can I change the tail position?

All vectors are drawn starting from the origin for clear visual addition; only the tip is movable.

What does the resultant color represent?

The resultant is drawn in cyan with a thicker arrow. Its magnitude and direction are shown in the overlay.

How are components calculated?

Each vector's tip coordinates (x,y) are its components. The resultant components are the sums of all x and y values.

Can I see the angle of each vector?

Yes, the component table (if toggled on) shows each vector's magnitude and angle (from positive x-axis).