Equation of the line passing through the point (0,1,2) and equally inclined to the coordintate axes, are

Options

A. x=y-1=z-2
B. x=y+1=z+2
C. `x/0=y/3=z/2`
D. None of these

Explanation

To find the equation of the line passing through the point (0, 1, 2) and equally inclined to the coordinate axes, we can follow these steps:

### Step 1: Understand the Condition of Equally Inclined
The line is said to be equally inclined to the coordinate axes. This means that the direction cosines of the line with respect to the x, y, and z axes are equal. Let's denote the direction cosines as \( l, m, n \). Therefore, we have:
\[ l = m = n = k \]
for some constant \( k \).

### Step 2: Use the Point and Direction Cosines
The line passes through the point \( (0, 1, 2) \). The general equation of a line in three-dimensional space that passes through a point \( (x_1, y_1, z_1) \) with direction ratios \( (l, m, n) \) is given by:
\[ \frac{x - x_1}{l} = \frac{y - y_1}{m} = \frac{z - z_1}{n} \]
Substituting the point \( (0, 1, 2) \) into the equation, we get:
\[ \frac{x - 0}{k} = \frac{y - 1}{k} = \frac{z - 2}{k} \]

### Step 3: Simplify the Equation
Since \( l = m = n = k \), we can simplify the equation:
\[ \frac{x}{k} = \frac{y - 1}{k} = \frac{z - 2}{k} \]
Multiplying through by \( k \) (assuming \( k \neq 0 \)):
\[ x = y - 1 = z - 2 \]

### Step 4: Write the Final Equation
We can express the relationships derived from the previous step as:
\[ x = y - 1 \quad \text{and} \quad y - 1 = z - 2 \]
Thus, the final equation of the line can be written as:
\[ x = y - 1 = z - 2 \]

### Conclusion
The equation of the line passing through the point \( (0, 1, 2) \) and equally inclined to the coordinate axes is:
\[ x = y - 1 = z - 2 \]