Confusing parallel with collinear H
"The Parallel Pitfall"
The Mistake in Action
Prove A, B, and C are collinear. Student shows $\vec{AB} = 2\mathbf{a}$ and $\vec{CD} = 4\mathbf{a}$. Conclusion: "They are collinear."
Why It Happens
Students successfully prove the vectors are parallel but apply the wrong terminology or logic. Collinear means "on the same line", not just parallel.
The Fix
To prove Collinear:
- Show vectors are parallel (e.g. $\vec{AC} = 2\vec{AB}$)
- State that they share a common point (B).
Without the common point, the lines could just be parallel like train tracks.
Spot the Mistake
Can you identify where this student went wrong?
Prove A, B, C are collinear
AB = a + b, BC = 2(a + b)
Vectors are parallel, so points are collinear
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: