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Exam Response (vectors)
Typical tasks: |a|; unit vector; AB=b-a; a·b and theta; a x b from the ijk det; area; a·(b x c) volume; perp vs parallel tests. Show the 3x3 expansion with the minus on j. One component per line is fine.
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Exam Response (vectors)
What is it?
Typical tasks: |a|; unit vector; AB=b-a; a·b and theta; a x b from the ijk det; area; a·(b x c) volume; perp vs parallel tests. Show the 3x3 expansion with the minus on j. One component per line is fine.
In simple words
- Typical tasks: |a|; unit vector; AB=b-a; a·b and theta; a x b from the ijk det; area; a·(b x c) volume; perp vs parallel tests.
- Show the 3x3 expansion with the minus on j.
- One component per line is fine.
- Do not use a x b when the question asks for work (that is a dot).
Important terms
EXAM RESPONSE (VECTORS): Typical tasks: |a|; unit vector; AB=b-a; a·b and theta; a x b from the ijk det; area; a·(b x c) volume; perp vs parallel tests. Show the 3x3 expansion with the minus on j. One component per line is fine.
1. TESTS: perp: dot 0. parallel: cross 0. coplanar: triple 0. unit: divide by |a|.
2. COMPUTE: Dot: sum products. Cross: ijk det. Triple: 3x3 det of the three vectors.
What you should learn
- State the main ideas and notation used in exam response (vectors).
- Apply the rules of exam response (vectors) in a clear, step-by-step solution.
- Check signs, conditions, and the final answer for mathematical accuracy.
Examples
- a·b=0
- a x b=0
- det=0
TESTS
perp: dot 0. parallel: cross 0. coplanar: triple 0. unit: divide by |a|.
COMPUTE
Dot: sum products. Cross: ijk det. Triple: 3x3 det of the three vectors.
Recommended for Class 11
Full school-level explanation
Typical tasks: |a|; unit vector; AB=b-a; a·b and theta; a x b from the ijk det; area; a·(b x c) volume; perp vs parallel tests. Show the 3x3 expansion with the minus on j. One component per line is fine.
Tests, then a product:
WHAT — EXAM RESPONSE (VECTORS)
Typical tasks: |a|; unit vector; AB=b-a; a·b and theta; a x b from the ijk det; area; a·(b x c) volume; perp vs parallel tests. Show the 3x3 expansion with the minus on j. One component per line is fine.
RULE — 1. TESTS
perp: dot 0. parallel: cross 0. coplanar: triple 0. unit: divide by |a|.
METHOD — 2. COMPUTE
Dot: sum products. Cross: ijk det. Triple: 3x3 det of the three vectors.
WORKED EXAMPLE
Worked 4-mark perp check. a=<1,2,-1>, b=<2,-1,0> a·b = 2 - 2 + 0 = 0 so a perp b (neither is 0)
TESTS
perp: dot 0. parallel: cross 0. coplanar: triple 0. unit: divide by |a|.
Remember
- zero tests
Examples
- a·b=0
- a x b=0
- det=0
COMPUTE
Dot: sum products. Cross: ijk det. Triple: 3x3 det of the three vectors.
Remember
- write the matrix
Examples
- cos theta
- area |cross|
- volume |triple|
How to answer a exam response (vectors) question
How it works
- Identify the given quantities, notation, and required result.
- Choose the matching rule and write it before substitution.
- Work one algebraic step at a time, keeping brackets and signs clear.
- Check restrictions, simplify the result, and verify it where possible.
Remember
- dot = scalar, cross = vector
- AB = b-a
- dot 0
- match the product
- zero tests
- write the matrix
- dot = scalar, cross = vector
- AB = b-a
How the ideas connect
Worked 4-mark perp check. a=<1,2,-1>, b=<2,-1,0> a·b = 2 - 2 + 0 = 0 so a perp b (neither is 0)
Deeper understanding
Go beyond memorising Exam Response (vectors). Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked 4-mark perp check. a=<1,2,-1>, b=<2,-1,0> a·b = 2 - 2 + 0 = 0 so a perp b (neither is 0)
Common mistakes
Exam focus
Core Idea
1. TESTS
2. COMPUTE
Worked Example
Exam focus
Quick revision
- dot = scalar, cross = vector
- AB = b-a
- dot 0
- match the product
- EXAM RESPONSE (VECTORS): Typical tasks: |a|; unit vector; AB=b-a; a·b and theta; a x b from the ijk det; area; a·(b x c) volu
- 1. TESTS: perp: dot 0. parallel: cross 0. coplanar: triple 0. unit: divide by |a|.
Do not use a x b when the question asks for work (that is a dot).
For long answers on Exam Response (vectors): define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- dot = scalar, cross = vector
- AB = b-a
- dot 0
- match the product
Important formulas
- dot = scalar, cross = vector
- AB = b-a
- dot 0
Common exam traps
- Do not use a x b when the question asks for work (that is a dot).
- Do not use a remembered formula before checking that its conditions fit the question.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Do not use a x b when the question asks for work (that is a dot).
- Mistake
Do not use a remembered formula before checking that its conditions fit the question.
- Mistake
Do not hide sign changes or restrictions; write them on the line where they are used.
- Mistake
Do not use a x b when the question asks for work (that is a dot).
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
dot = scalar, cross = vector
AB = b-a
dot 0
match the product
Typical tasks: |a|; unit vector; AB=b-a; a·b and theta; a x b from the ijk det; area; a·(b x c) volume; perp vs parallel tests. Show the 3x3 expansion with the
dot = scalar, cross = vector
- Definition
- Typical tasks: |a|; unit vector; AB=b-a; a·b and theta; a x b from the ijk det; area; a·(b x c) volume; perp vs parallel tests. Show the 3x3 expansion with the
- Formula
- dot = scalar, cross = vector
- Example
- a·b=0
- Critical warning
- Do not use a x b when the question asks for work (that is a dot).
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Exam Practice
Define
Q1. Define Exam Response (vectors).
Explain
Q2. Explain: TESTS.
Example
Q3. Give one clear example of Exam Response (vectors) and say why it fits.
Mistake
Q4. State one common mistake students make about Exam Response (vectors).
Exam note
Q5. Write a short exam note on Exam Response (vectors): definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.