Class CBSE Class 12 Mathematics Vector Algebra Q #856
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
A unit vector along the vector $4\hat{i}-3\hat{k}$ is:
(A) $\frac{1}{7}(4\hat{i}-3\hat{k})$
(B) $\frac{1}{5}(4\hat{i}-3\hat{k})$
(C) $\frac{1}{\sqrt{7}}(4\hat{i}-3\hat{k})$
(D) $\frac{1}{\sqrt{5}}(4\hat{i}-3\hat{k})$
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Correct Answer: B

AI Tutor Explanation

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Step-by-Step Solution

  1. First, find the magnitude of the vector $4\hat{i}-3\hat{k}$.

    Magnitude = $\sqrt{(4)^2 + (0)^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5$

  2. Next, divide the vector by its magnitude to find the unit vector.

    Unit vector = $\frac{4\hat{i}-3\hat{k}}{5} = \frac{1}{5}(4\hat{i}-3\hat{k})$

Correct Answer: $\frac{1}{5}(4\hat{i}-3\hat{k})$

AI Suggestion: Option B

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the formula for finding a unit vector.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure to calculate the unit vector.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests knowledge of vector operations as covered in the textbook.

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