Class CBSE Class 12 Mathematics Vector Algebra Q #561
KNOWLEDGE BASED
APPLY
1 Marks 2025 AISSCE(Board Exam) MCQ SINGLE
If \(|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|\) for any two vectors, then vectors \(\vec{a}\) and \(\vec{b}\) are:
(A) orthogonal vectors
(B) parallel to each other
(C) unit vectors
(D) collinear vectors
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AI Tutor Explanation

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Step-by-Step Solution

  1. Given: \(|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|\)
  2. Squaring both sides: \(|\vec{a}+\vec{b}|^2=|\vec{a}-\vec{b}|^2\)
  3. Expanding using the dot product: \((\vec{a}+\vec{b})\cdot(\vec{a}+\vec{b}) = (\vec{a}-\vec{b})\cdot(\vec{a}-\vec{b})\)
  4. \(\vec{a}\cdot\vec{a} + 2\vec{a}\cdot\vec{b} + \vec{b}\cdot\vec{b} = \vec{a}\cdot\vec{a} - 2\vec{a}\cdot\vec{b} + \vec{b}\cdot\vec{b}\)
  5. Simplifying: \(4\vec{a}\cdot\vec{b} = 0\)
  6. \(\vec{a}\cdot\vec{b} = 0\)
  7. This implies that the vectors \(\vec{a}\) and \(\vec{b}\) are orthogonal (perpendicular).

Correct Answer: orthogonal vectors

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 properties of vector addition and subtraction, along with the concept of magnitude, to deduce the relationship between the two vectors.
Knowledge Dimension: CONCEPTUAL
Justification: The question requires understanding the concepts of vector magnitude, addition, subtraction, and orthogonality to arrive at the correct answer. It's not just recalling a fact but applying the understanding of these concepts.
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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