Class CBSE Class 12 Mathematics Vector Algebra Q #818
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
The value of p for which the vectors 2\hat{i}+p\hat{j}+\hat{k} and -4\hat{i}-6\hat{j}+26\hat{k} are perpendicular to each other, is:
(A) 3
(B) \-3
(C) -\frac{17}{3}
(D) \frac{17}{3}
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Step-by-Step Solution

Let the two vectors be \(\vec{a} = 2\hat{i} + p\hat{j} + \hat{k}\) and \(\vec{b} = -4\hat{i} - 6\hat{j} + 26\hat{k}\).

Since the vectors are perpendicular, their dot product is zero: \(\vec{a} \cdot \vec{b} = 0\).

Calculate the dot product: \((2\hat{i} + p\hat{j} + \hat{k}) \cdot (-4\hat{i} - 6\hat{j} + 26\hat{k}) = 0\)

This gives: \((2 \times -4) + (p \times -6) + (1 \times 26) = 0\)

Simplify: \(-8 - 6p + 26 = 0\)

Further simplification: \(-6p + 18 = 0\)

Solve for p: \(-6p = -18\)

Therefore, \(p = \frac{-18}{-6} = 3\)

Correct Answer: 3

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 concept of perpendicular vectors and their dot product to find the unknown value 'p'.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure (calculating the dot product and setting it to zero) to arrive at the solution.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding of vector algebra concepts as covered in the textbook.

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