Class CBSE Class 12 Mathematics Vector Algebra Q #819
KNOWLEDGE BASED
UNDERSTAND
1 Marks 2023 MCQ SINGLE
The value of (\hat{i}\times\hat{j})\cdot \hat{j}+(\hat{j}\times\hat{i}) \hat{k}:
(A) 2
(B) 0
(C) 1
(D) \-1
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AI Tutor Explanation

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Step-by-Step Solution

First, we evaluate the cross products:

  1. \(\hat{i} \times \hat{j} = \hat{k}\)
  2. \(\hat{j} \times \hat{i} = -\hat{k}\)

Next, we evaluate the dot products:

  1. \((\hat{i}\times\hat{j})\cdot \hat{j} = \hat{k} \cdot \hat{j} = 0\)
  2. \((\hat{j}\times\hat{i}) \cdot \hat{k} = -\hat{k} \cdot \hat{k} = -1\)

Finally, we add the results:

\(0 + (-1) = -1\)

Correct Answer: -1

AI Suggestion: Option D

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Pedagogical Audit
Bloom's Analysis: This is an UNDERSTAND question because it requires students to recall and apply the properties of cross and dot products of unit vectors.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to execute a sequence of steps involving the cross product and dot product of vectors.
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 as covered in the textbook.

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