Direction-cosines of z-axis are ................. .

Answer

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

### Step-by-Step Solution:

1. **Understanding Direction Ratios**:
- The direction ratios of the z-axis can be represented as (0, 0, 1). This means that the x and y components are 0, and the z component is 1.

2. **Calculating the Modulus of the Direction Ratios**:
- The modulus (or magnitude) of the direction ratios can be calculated using the formula:
\[ \text{Modulus} = \sqrt{x^2 + y^2 + z^2} \]
- Substituting the values of the direction ratios:
\[ \text{Modulus} = \sqrt{0^2 + 0^2 + 1^2} = \sqrt{0 + 0 + 1} = \sqrt{1} = 1 \]

3. **Finding Direction Cosines**:
- The direction cosines are found by dividing each component of the direction ratios by the modulus:
\[ \text{Direction Cosines} = \left( \frac{x}{\text{Modulus}}, \frac{y}{\text{Modulus}}, \frac{z}{\text{Modulus}} \right) \]
- Substituting the values:
\[ \text{Direction Cosines} = \left( \frac{0}{1}, \frac{0}{1}, \frac{1}{1} \right) = (0, 0, 1) \]

4. **Final Result**:
- Therefore, the direction cosines of the z-axis are:
\[ (0, 0, 1) \]

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

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