Vectors — Definition, Notation, and Components
What is a vector?
A vector has magnitude and direction. We can write a vector in several ways:
- Boldface: v
- Arrow notation: v⃗ (read “vector v”)
- Components:
(vx, vy)in the x–y plane
Scalars vs. Vectors. A scalar has size only (e.g., mass 3 kg). A vector has size and direction
(e.g., displacement (4, −2)).
Length (magnitude) of a vector — no trig needed
For v = (vx, vy):
|v| = √[(vx)² + (vy)²]
Example. v = (−3, 4) → |v| = √( (−3)² + 4² ) = √(9 + 16) = √25 = 5
Interactive — Add & Subtract Vectors by Components
Click on the plane to add vectors tip-to-tail, or enter components to add. Axes run from −100 to +100. No angles—just components and length.
Core Practice — Vector Components (5 rounds)
Add/subtract using components only (no angles). Enter exact integers for Rx, Ry; magnitude can be a decimal (small rounding ok).
Click “New Round”.
More Practice (6 questions, need ≥5 correct)
No angles. You’ll add/subtract components and compute magnitudes.
✅ More practice complete! (≥ 5/6)
❌ Need at least 5/6. Keep going!