If a, b, c are the angles that a line makes with the positive directions of x, y and z axis, respectively, then the direction cosines of the lines are

Options

A. sin a, sin b, sin c
B. cos a, cos b, cos c
C. tan a, tan b, tan c
D. none of the above

Answer

To find the direction cosines of a line that makes angles \( a \), \( b \), and \( c \) with the positive directions of the \( x \)-axis, \( y \)-axis, and \( z \)-axis respectively, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Direction Cosines**:
The direction cosines of a line are the cosines of the angles that the line makes with the coordinate axes. If a line makes angles \( a \), \( b \), and \( c \) with the \( x \)-axis, \( y \)-axis, and \( z \)-axis respectively, then the direction cosines are defined as:
\[ l = \cos a, \quad m = \cos b, \quad n = \cos c \]
where \( l \), \( m \), and \( n \) are the direction cosines corresponding to the \( x \), \( y \), and \( z \) axes.

2. **Applying the Definition**:
Based on the definition, we can directly write the direction cosines:
\[ \text{Direction cosines} = (\cos a, \cos b, \cos c) \]

3. **Conclusion**:
Therefore, the direction cosines of the line are:
\[ (\cos a, \cos b, \cos c) \]

### Final Answer:
The direction cosines of the line are \( \cos a, \cos b, \cos c \).

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