Which of the following represents direction cosines of the line ?

Options

A. `0,(1)/(sqrt(2)),(1)/(2)`
B. `0,-(sqrt(3))/(2),(1)/(sqrt(2))`
C. `0,(sqrt(3))/(2),(1)/(2)`
D. `(1)/(2),(1)/(2),(1)/(2)`

Explanation

To determine which of the given options represents the direction cosines of a line, we need to check if the sum of the squares of the proposed direction cosines equals 1. The direction cosines of a line are typically denoted as \( l, m, n \) and they must satisfy the equation:

\[ l^2 + m^2 + n^2 = 1 \]

Let's analyze each option step by step.

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