Class CBSE Class 12 Mathematics Three Dimensional Geometry Q #667
KNOWLEDGE BASED
APPLY
1 Marks 2024 AISSCE(Board Exam) MCQ SINGLE
Direction ratios of a vector parallel to line \(\frac{x-1}{2}=-y=\frac{2z+1}{6}\) are:
(A) \(2,-1,6\)
(B) \(2, 1, 6\)
(C) \(2, 1, 3\)
(D) \(2,-1, 3\)
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Correct Answer: D

AI Tutor Explanation

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Step-by-Step Solution

  1. Rewrite the given equation in the standard form: \(\frac{x-1}{2} = \frac{y}{-1} = \frac{z + \frac{1}{2}}{3}\)
  2. The direction ratios are the coefficients in the denominator. Therefore, the direction ratios are \(2, -1, 3\).

Correct Answer: D<\/strong>

AI Suggestion: Option D

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply their knowledge of direction ratios and how to manipulate the given equation of a line to find the correct direction ratios.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure to first standardize the equation of the line and then identify the direction ratios.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding of direction ratios and the equation of a line in 3D space, which is a core concept covered in the textbook.

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