Question

The direction cosines of the line which bisects the angle between the positive direction of Y and Z axes are

• A. \( \frac{1}{\sqrt{2}}, 0, \frac{1}{\sqrt{2}} \)
• B. \( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0 \)
• C. \( 0, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \)
• D. \( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \)

Hint:

The direction cosines of a line bisecting the angle between two axes are equal for those two axes and zero for the axis perpendicular to them.

Answer 1

The Correct Option is C

Step 1: Understanding the concept of direction cosines.
The direction cosines of a line are the cosines of the angles that the line makes with the coordinate axes. To bisect the angle between the positive directions of the Y and Z axes, the direction cosines must be equal for the Y and Z axes and zero for the X axis, since the line lies in the Y-Z plane. Thus, the direction cosines are \( 0, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \).

Step 2: Conclusion.
Thus, the correct answer is \( 0, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \), corresponding to option (C).