MathematicsChapter 3: Vectors
I J K Table
Cyclic i->j->k->i. Opposite cycle gives a minus.
Learning objectives
- State the rule or meaning of i j k table in easy words.
- Apply i j k table in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Definition
Cyclic i->j->k->i. Opposite cycle gives a minus. These three lines are the exam memory: i x j = k, j x k = i, k x i = j.
Mathematical form
j = k
k = i
i = j.
Where / symbols
- I J K TABLE
- Cyclic i->j->k->i. Opposite cycle gives a minus. These three lines are the exam memory: i x j = k, j x k = i, k x i = j.
- i j k TABLE
- Cyclic i->j->k->i.
Relationship
- |a x b| = |a||b| sin theta
Overview
Understand the idea, then apply it:
Main Idea
Cyclic i->j->k->i. Opposite cycle gives a minus. These three lines are the exam memory: i x j = k, j x k = i, k x i = j.
Examples i x j = k · j x i = -k · i x i = 0
Exam Use
Write the rule first: Cyclic i->j->k->i. 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 — I J K TABLE
Cyclic i->j->k->i. Opposite cycle gives a minus. These three lines are the exam memory: i x j = k, j x k = i, k x i = j.
WHY — Why it matters
This rule is a separate learning unit inside cross (vector) product. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: Cyclic i->j->k->i. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
How to answer a i j k table 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
Cross is not commutative. Swapping order changes sign.
Key points
- cyclic plus
- |a x b| = |a||b| sin theta
- direction: right hand
- focused answer
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.I J K Table
Sticky Notes · Quick Revision
Core Idea
- Cyclic i->j->k->i.
What to Know
- Cyclic i->j->k->i. Opposite cycle gives a minus. These three lines are the exam memory: i x j = k, j x k = i, k x i = j.
Example or Evidence
- i x j = k
- j x i = -k
- i x i = 0
How to Answer
- Write the rule first: Cyclic i->j->k->i. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Common Error
- Cross is not commutative. Swapping order changes sign.
FBISE Exam Check
- State the rule, show the working, and check the answer.
60-second revision
- Cyclic i->j->k->i.
- i x j = k
- j x i = -k
- State the rule, show the working, and check the answer.
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