Question

The direction cosines of z-axis are:

• A. 1,0,0
• B. 0,1,0
• C. 0,0,1
• D. 1,1,1

Answer 1

The Correct Option is C

The direction cosines of a line in three-dimensional space are the cosines of the angles that the line makes with the positive x, y, and z axes. For the z-axis itself, these cosines can be determined as follows:

1. The z-axis is parallel to the vector (0,0,1).
2. The cosine of the angle with the x-axis is given by the x-component of the unit vector parallel to the z-axis, which is 0.
3. The cosine of the angle with the y-axis is given by the y-component of the unit vector parallel to the z-axis, which is also 0.
4. The cosine of the angle with the z-axis is given by the z-component of the unit vector, which is 1.

Therefore, the direction cosines of the z-axis are 0,0,1, which corresponds to the option

0,0,1

.