MathematicsChapter 7: Vectors in Plane
Parallel
The zero vector 0 has length 0 and is the identity for addition: u+0=u.
Learning objectives
- Define and explain parallel.
- Apply parallel to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
The zero vector 0 has length 0 and is the identity for addition: u+0=u. Non-zero vectors are parallel if one is a scalar times the other (including a negative scalar, which is anti-parallel). [2,1] and [4,2] are parallel because [4,2]=2[2,1].
Where / symbols
- Parallel
- The zero vector 0 has length 0 and is the identity for addition: u+0=u. Non-zero vectors are parallel if one is a scalar times the other (including a negative scalar, which is anti-parallel). [2,1] and [4,2] are parallel because [4,2]=2[2,1].
Overview
Learn the idea, then use it:
Core Understanding
The zero vector 0 has length 0 and is the identity for addition: u+0=u. Non-zero vectors are parallel if one is a scalar times the other (including a negative scalar, which is anti-parallel). [2,1] and [4,2] are parallel because [4,2]=2[2,1].
Examples 0 has length 0 · parallel: scalar multiple
Exam Application
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
WHAT — PARALLEL
The zero vector 0 has length 0 and is the identity for addition: u+0=u. Non-zero vectors are parallel if one is a scalar times the other (including a negative scalar, which is anti-parallel). [2,1] and [4,2] are parallel because [4,2]=2[2,1].
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
In simple words
Do not merge parallel with a neighbouring idea that uses a different definition, rule, or method.
Key points
- 0 has length 0
- parallel: scalar multiple
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Parallel
Sticky Notes · Quick Revision
Core Idea
- The zero vector 0 has length 0 and is the identity for addition: u+0=u.
Key Points
- 0 has length 0
- parallel: scalar multiple
Simple Check
- Explain parallel in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge parallel with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- The zero vector 0 has length 0 and is the identity for addition: u+0=u.
- 0 has length 0
- parallel: scalar multiple
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