Class CBSE Class 12 Mathematics Vector Algebra Q #568
KNOWLEDGE BASED
APPLY
1 Marks 2025 AISSCE(Board Exam) MCQ SINGLE
The projection vector of vector \(\vec{a}\) on vector \(\vec{b}\) is
(A) \((\frac{\vec{a}\cdot\vec{b}}{|\vec{b}|^{2}})\vec{b}\)
(B) \(\frac{\vec{a}\cdot\vec{b}}{|\vec{b}|}\)
(C) \(\frac{\vec{a}\cdot\vec{b}}{|\vec{a}|}\)
(D) \((\frac{\vec{a}\cdot\vec{b}}{|\vec{a}|^{2}})\vec{b}\)
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Correct Answer: A
Explanation
\((\frac{\vec{a}\cdot\vec{b}}{|\vec{b}|^{2}})\vec{b}\)

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Step-by-Step Solution

  1. The projection vector of vector \(\vec{a}\) on vector \(\vec{b}\) is given by the formula: \[ \text{proj}_{\vec{b}} \vec{a} = \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|^2} \vec{b} \]
  2. Comparing the given options with the formula, we find that option (A) matches the correct formula.

Correct Answer: \((\frac{\vec{a}\cdot\vec{b}}{|\vec{b}|^{2}})\vec{b}\)

AI Suggestion: Option A

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the formula for the projection of one vector onto another.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to execute a procedure, which is applying the formula for the projection of a vector onto another vector.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the recall and application of a standard formula from the textbook.

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