A plane II makes intercept 3 and 4 respectively on `x` and `z` axes. If II is parallel to y-axis, then its equation is

Options

A. `3x+4y=12`
B. `4x+3z=12`
C. `3y+4z=12`
D. `4y+3y=12`

Explanation

To find the equation of the plane that makes intercepts of 3 and 4 on the x and z axes respectively and is parallel to the y-axis, we can follow these steps:

### Step 1: Understand the intercept form of the plane equation
The general equation of a plane in intercept form is given by:
\[ \frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1 \]
where \(a\), \(b\), and \(c\) are the intercepts on the x, y, and z axes respectively.

### Step 2: Identify the intercepts
From the problem, we know:
- The x-intercept \(a = 3\)
- The z-intercept \(c = 4\)
- The plane is parallel to the y-axis, which implies that the y-intercept \(b = 0\).

### Step 3: Substitute the intercepts into the equation
Since the plane is parallel to the y-axis, we can set \(b = 0\). Thus, the equation becomes:
\[ \frac{x}{3} + \frac{y}{0} + \frac{z}{4} = 1 \]
However, since \(b = 0\), the term \(\frac{y}{0}\) is undefined. To handle this, we can express the equation without the y term:
\[ \frac{x}{3} + \frac{z}{4} = 1 \]

### Step 4: Rearranging the equation
To eliminate the fractions, we can multiply the entire equation by 12 (the least common multiple of 3 and 4):
\[ 12 \left( \frac{x}{3} + \frac{z}{4} \right) = 12 \cdot 1 \]
This simplifies to:
\[ 4x + 3z = 12 \]

### Step 5: Final equation of the plane
Thus, the equation of the plane is:
\[ 4x + 3z = 12 \]

### Summary
The equation of the plane that makes intercepts of 3 and 4 on the x and z axes and is parallel to the y-axis is:
\[ 4x + 3z = 12 \]