Class CBSE Class 12 Mathematics Three Dimensional Geometry Q #669
KNOWLEDGE BASED
UNDERSTAND
1 Marks 2024 AISSCE(Board Exam) MCQ SINGLE
The distance of point \(P(a,b,c)\) from y-axis is :
(A) b
(B) \(b^{2}\)
(C) \(\sqrt{a^{2}+c^{2}}\)
(D) \(a^{2}+c^{2}\)
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Correct Answer: C

AI Tutor Explanation

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Step-by-Step Solution

To find the distance of a point \(P(a, b, c)\) from the y-axis, we need to consider the projection of the point onto the xz-plane. The coordinates of the projection will be \((a, 0, c)\).

The distance from the point \(P(a, b, c)\) to the y-axis is the distance between the point \((a, 0, c)\) and the origin in the xz-plane, which is given by the formula:

\(\sqrt{(a - 0)^{2} + (0 - 0)^{2} + (c - 0)^{2}} = \sqrt{a^{2} + c^{2}}\)

Correct Answer: \(\sqrt{a^{2}+c^{2}}\)

AI Suggestion: Option C

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Pedagogical Audit
Bloom's Analysis: This is an UNDERSTAND question because it requires students to recall and explain the concept of distance from a point to an axis in 3D space.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of the concept of distance of a point from the y-axis in a 3-dimensional coordinate system. It involves knowing the formula and applying it correctly.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly assesses the student's understanding of a specific formula or concept taught in the textbook.

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