What are the direction cosines of z axis?

Options

A. `lt1,1,1gt`
B. `lt1,0,0gt`
C. `lt0,1,1gt`
D. `lt0,0,1gt`

Answer

To find the direction cosines of the z-axis, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Direction Cosines**:
Direction cosines are the cosines of the angles that a vector makes with the coordinate axes. For a vector along the z-axis, we need to determine the angles it makes with the x-axis and y-axis.

2. **Identify the Axes**:
- The x-axis is horizontal.
- The y-axis is also horizontal but perpendicular to the x-axis.
- The z-axis is vertical and perpendicular to both the x-axis and y-axis.

3. **Angles with the Axes**:
- The angle between the z-axis and the x-axis (let's call it α) is 90 degrees.
- The angle between the z-axis and the y-axis (let's call it β) is also 90 degrees.
- The angle between the z-axis and itself (let's call it γ) is 0 degrees.

4. **Calculating the Direction Cosines**:
- The direction cosine along the x-axis (L) is given by cos(α):
\[ L = \cos(90^\circ) = 0 \]
- The direction cosine along the y-axis (M) is given by cos(β):
\[ M = \cos(90^\circ) = 0 \]
- The direction cosine along the z-axis (N) is given by cos(γ):
\[ N = \cos(0^\circ) = 1 \]

5. **Final Result**:
- Therefore, the direction cosines of the z-axis are:
\[ (L, M, N) = (0, 0, 1) \]

### Conclusion:
The direction cosines of the z-axis are \(0, 0, 1\).

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