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Vectors and 3D Geometry

Direction Cosines

jee_main_2026_jan_22_shift_1

Grade None

Question:

If the direction cosines of a line are \(l, m, n\) and \(l^2 + m^2 + n^2 = 1\), then the value of \(l^2 + m^2\) is:

A. 1 - n²

B. 1 + n²

C. 0

D. n²

Step-by-Step Solution

Key Concept: Direction cosines satisfy \(l^2 + m^2 + n^2 = 1\).

Step 1: \(l^2 + m^2 + n^2 = 1\). Step 2: \(l^2 + m^2 = 1 - n^2\).

Correct Answer: A

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