The plane V
 is described by the equation (−1)⋅x+0⋅y+0⋅z=−1
.

Find a parameter equation for V
.

The equation of the plane is given as:

\[
-1 \cdot x + 0 \cdot y + 0 \cdot z = -1
\]

This simplifies to:

\[
x = 1
\]

This means that the plane \( V \) is a vertical plane where \( x = 1 \) and it extends indefinitely in the \( y \)- and \( z \)-directions. In other words, \( y \) and \( z \) can take any values, but \( x \) is fixed at 1.

### Parametric Equation of the Plane

To express this plane in parametric form, we can write:

\[
\mathbf{r}(t_1, t_2) = (1, t_1, t_2)
\]

where \( t_1 \) and \( t_2 \) are free parameters corresponding to the coordinates \( y \) and \( z \), respectively.

Thus, the parametric equations for the plane \( V \) are:

\[
x = 1
\]
\[
y = t_1
\]
\[
z = t_2
\]

where \( t_1 \) and \( t_2 \) are any real numbers.

Would you like more details or have any further questions?

Here are 5 related questions:
1. How do you determine the parametric form for a general plane?
2. Can you describe how the normal vector relates to the equation of a plane?
3. What are the differences between parametric and implicit forms of a plane?
4. How would you find the line of intersection between two planes?
5. How can you verify that a point lies on a given parametric plane?

**Tip:** When converting to parametric form, always identify which variables are free (parameters) and which are fixed or dependent.

The plane V is described by the equation (−1)⋅x+0⋅y+0⋅z=−1. Find a parameter equation for V.

Explore how to find the parametric equation for the plane described by x = 1. Understand key geometric concepts such as parametric equations and how they represent a plane in three-dimensional space. Suitable for high school students in Grades 10-12.

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