Class CBSE Class 12 Mathematics Vector Algebra Q #1850
COMPETENCY BASED
APPLY
1 Marks 2026 AISSCE(Board Exam) MCQ SINGLE
The value of p for which vectors $\hat{i} + 2\hat{j} + 3\hat{k}$ and $2\hat{i} - p\hat{j} + \hat{k}$ are perpendicular to each other is
(A) $0$
(B) $1$
(C) $\frac{5}{2}$
(D) $-\frac{5}{2}$
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Correct Answer: C

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Detailed Solution

Step 1: Identify the condition for perpendicular vectors

Two vectors a and b are perpendicular if and only if their dot product is zero. That is, a · b = 0.

Step 2: Set up the dot product equation

Given vectors are a = 1i + 2j + 3k and b = 2i - pj + 1k. The dot product is calculated as:

$$(1)(2) + (2)(-p) + (3)(1) = 0$$

Step 3: Solve for p

Simplify the equation:

$$2 - 2p + 3 = 0$$ $$5 - 2p = 0$$ $$2p = 5$$ $$p = \frac{5}{2}$$

Final Answer: 5/2

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student must utilize the mathematical definition of orthogonality (dot product = 0) to solve for an unknown variable.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the execution of a specific algorithm (dot product calculation) to reach the solution.
Syllabus Audit: In the context of CBSE Class 12, this is classified as COMPETENCY. This tests the fundamental understanding of vector algebra operations as prescribed in the Vector Algebra chapter.

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