 Identify the shape of the 3d surface: x + 3y - 4z = 7

The given equation is \( x + 3y - 4z = 7 \).

This equation represents a **plane** in three-dimensional space. 

### Reasoning:
- A plane in 3D space is generally represented by a linear equation of the form \( ax + by + cz = d \), where \( a \), \( b \), and \( c \) are coefficients, and \( d \) is a constant. 
- The given equation \( x + 3y - 4z = 7 \) is of this form, confirming that it is indeed a plane.

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Here are 5 related questions:
1. How do you find the normal vector of the plane \( x + 3y - 4z = 7 \)?
2. What is the distance from a point to the plane \( x + 3y - 4z = 7 \)?
3. How do you find the intercepts of the plane \( x + 3y - 4z = 7 \) with the coordinate axes?
4. How can you determine if two planes are parallel?
5. What is the intersection line of two planes in 3D space?

**Tip:** The normal vector of a plane \( ax + by + cz = d \) is given by the vector \( \vec{n} = \langle a, b, c \rangle \).

Identify the shape of the 3d surface: x + 3y - 4z = 7

Explore how to identify the shape of the 3D surface given by the equation x + 3y - 4z = 7. This problem focuses on the concepts of planes in three-dimensional space, suitable for high school students in Grades 10-12.

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