Det Form

Det Form

What is it?

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).

In simple words

• Write the 3x3 and expand.
• Rows = the three vectors
• Expand any row
• State the rule, show the working, and check the answer.

Important terms

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.

What you should learn

• 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.

Examples

• Rows = the three vectors
• Expand any row
• Check with a small example

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).

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.

Full school-level explanation

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).

Understand the idea, then apply it:

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.

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).

Remember

• 3x3 det

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.

Remember

• focused answer
• accurate support

Examples

• State the central idea
• Use one accurate detail
• Check the final response

How to answer a det form question

How it works

• 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.

Remember

• 3x3 det
• a·(b x c) = det[a b c]
• 0 => coplanar
• dot after cross
• 3x3 det
• focused answer
• accurate support
• 3x3 det

Deeper understanding

Go beyond memorising Det Form. Connect the definition to reasons, relationships, exceptions, and exam wording.

Common mistakes

Exam focus

Core Idea

What to Know

Example or Evidence

How to Answer

Exam focus

Quick revision

• 3x3 det
• a·(b x c) = det[a b c]
• 0 => coplanar
• dot after cross
• 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 brack
• DET FORM: Write the 3x3 and expand.

Triple product is a scalar. Brackets: a · (b x c), not (a · b) x c (that is illegal types).

For long answers on Det Form: define clearly → explain the main parts → give one example → state one exam caution.