Find the direction cosines of the z-axis.

The direction cosines of an axis represent the cosines of the angles that the axis makes with the three coordinate axes: x, y, and z. For the z-axis, the situation is quite straightforward.

Understanding Direction Cosines

Direction cosines are typically denoted as (l, m, n), where:

• l is the cosine of the angle with the x-axis
• m is the cosine of the angle with the y-axis
• n is the cosine of the angle with the z-axis

Direction Cosines of the Z-Axis

For the z-axis, the angles with the x and y axes are both 90 degrees, while the angle with itself is 0 degrees. The cosines of these angles are:

• Cosine of 90 degrees (with x-axis) = 0
• Cosine of 90 degrees (with y-axis) = 0
• Cosine of 0 degrees (with z-axis) = 1

Final Result

Thus, the direction cosines of the z-axis are:

(0, 0, 1)