Class CBSE Class 12 Mathematics Vector Algebra Q #820
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
If \vec{a}+\vec{b}=\hat{i} and \vec{a}=2\hat{i}-2\hat{j}+2\hat{k}, then |\vec{b}| equals:
(A) \sqrt{14}
(B) 3
(C) \sqrt{12}
(D) \sqrt{17}
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AI Tutor Explanation

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Step-by-Step Solution

  1. Given: \(\vec{a} + \vec{b} = \hat{i}\) and \(\vec{a} = 2\hat{i} - 2\hat{j} + 2\hat{k}\)
  2. We need to find \(\vec{b}\). From the given equation, \(\vec{b} = \hat{i} - \vec{a}\)
  3. Substitute the value of \(\vec{a}\): \(\vec{b} = \hat{i} - (2\hat{i} - 2\hat{j} + 2\hat{k})\)
  4. Simplify: \(\vec{b} = \hat{i} - 2\hat{i} + 2\hat{j} - 2\hat{k} = -\hat{i} + 2\hat{j} - 2\hat{k}\)
  5. Now, find the magnitude of \(\vec{b}\): \(|\vec{b}| = \sqrt{(-1)^2 + (2)^2 + (-2)^2}\)
  6. Calculate: \(|\vec{b}| = \sqrt{1 + 4 + 4} = \sqrt{9} = 3\)

Correct Answer: 3

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 concepts of vector addition and magnitude calculation to find the magnitude of vector b.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure to find the solution, which involves vector subtraction and magnitude calculation.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding and application of vector algebra concepts as covered in the textbook.

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