MathematicsChapter 3: Vectors
Det Form
Write the 3x3 and expand.
Learning objectives
- State the rule or meaning of det form in easy words.
- Apply det form in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Definition
Write the 3x3 and expand. a · (b x c) = (a x b) · c same value. Do not write a x b x c without brackets (not associated the same way).
Where / symbols
- DET FORM
- Write the 3x3 and expand. a · (b x c) = (a x b) · c same value. Do not write a x b x c without brackets (not associated the same way).
- DET FORM
- Write the 3x3 and expand.
Relationship
- a·(b x c) = det[a b c]
- 0 => coplanar
Overview
Understand the idea, then apply it:
Main Idea
Write the 3x3 and expand. a · (b x c) = (a x b) · c same value. Do not write a x b x c without brackets (not associated the same way).
Examples Rows = the three vectors · Expand any row · Check with a small example
Exam Use
Write the rule first: Write the 3x3 and expand. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Examples State the central idea · Use one accurate detail · Check the final response
WHAT — DET FORM
Write the 3x3 and expand. a · (b x c) = (a x b) · c same value. Do not write a x b x c without brackets (not associated the same way).
WHY — Why it matters
This rule is a separate learning unit inside scalar triple product. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: Write the 3x3 and expand. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
How to answer a det form question
- Read the exact command word and identify what the question asks.
- State the matching idea, rule, or meaning before adding detail.
- Use the unit evidence or mathematical working that directly supports the answer.
- Check accuracy, relevance, and answer length before finishing.
In simple words
Triple product is a scalar. Brackets: a · (b x c), not (a · b) x c (that is illegal types).
Key points
- 3x3 det
- a·(b x c) = det[a b c]
- 0 => coplanar
- focused answer
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Det Form
Sticky Notes · Quick Revision
Core Idea
- Write the 3x3 and expand.
What to Know
- Write the 3x3 and expand. a · (b x c) = (a x b) · c same value. Do not write a x b x c without brackets (not associated the same way).
Example or Evidence
- Rows = the three vectors
- Expand any row
- Check with a small example
How to Answer
- Write the rule first: Write the 3x3 and expand. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Common Error
- Triple product is a scalar. Brackets: a · (b x c), not (a · b) x c (that is illegal types).
FBISE Exam Check
- State the rule, show the working, and check the answer.
60-second revision
- Write the 3x3 and expand.
- Rows = the three vectors
- Expand any row
- State the rule, show the working, and check the answer.
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