Class CBSE Class 12 Mathematics Three Dimensional Geometry Q #821
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
If a line makes angles of 90°, 135° and 45° with the x, y and z axes respectively, then its direction cosines are
(A) 0, -1/√2, 1/√2
(B) -1/√2, 0, 1/√2
(C) 1/√2, 0, -1/√2
(D) 0, 1/√2, 1/√2
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Step-by-Step Solution

Let the direction cosines be l, m, and n.

Given the angles α = 90°, β = 135°, and γ = 45° with the x, y, and z axes respectively.

We know that l = cos α, m = cos β, and n = cos γ.

l = cos 90° = 0

m = cos 135° = cos (180° - 45°) = -cos 45° = -1/√2

n = cos 45° = 1/√2

Therefore, the direction cosines are 0, -1/√2, 1/√2.

Correct Answer: 0, -1/√2, 1/√2

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the formula for direction cosines given the angles with the axes.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure (applying the cosine function to the given angles) to calculate the direction cosines.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the knowledge of direction cosines and their relationship with angles made by a line with the coordinate axes, a concept covered in the textbook.

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