Question

The direction cosines of \( x \), \( y \), and \( z \)-axis are \(\underline{\hspace{2cm}}\) respectively.

Hint:

For the coordinate axes, the direction cosines are always 1 for the axis and 0 for the others.

Answer 1

Step 1: Definition of direction cosines.
The direction cosines of the coordinate axes \( x \), \( y \), and \( z \) are the cosines of the angles that the respective axes make with the coordinate axes. The direction cosines of the \( x \)-axis, \( y \)-axis, and \( z \)-axis are: \[ \cos \alpha = 1, \cos \beta = 0, \cos \gamma = 0. \]

Step 2: Conclusion.
Thus, the direction cosines of the \( x \), \( y \), and \( z \)-axes are 1, 0, and 0 respectively.