Common Mistakes
Frequent Errors
1. Treating vector `<a,b>` as point (a,b) without tail context (4.8.A.2). 2. Computing head minus tail as tail minus head (4.8.A.2). 3. Adding magnitudes instead of components (4.8.B.2). 4. Scalar multiply applied to magnitude only, not both components (4.8.B.1). 5. Dot product computed without matching components (4.8.B.3). 6. Unit vector missing division by magnitude (4.8.C.1). 7. Claiming perpendicular without checking dot product zero (4.8.D.1). 8. Ignoring zero vector case `<0,0>` (4.8.A.2).
Why These Happen
Students mix scalar and vector operations or skip diagrams.
How to Fix Them
- Always write tail -> head for components.
- Add `<a1,b1> + <a2,b2>` component-wise.
- Verify perpendicularity with dot product.
Avoidance Scripts
- "Head minus tail for components."
- "Dot before you claim perpendicular."
- "Unit vector keeps direction."
Quick Self-Check
- Did I subtract points in tail-to-head order?
- Did I operate on both components?
- Did I divide by magnitude for a unit vector?