Determine the equation of the line parallel to the y-axis through the point p (3/2/0)

A line that is parallel to the y-axis in three-dimensional space (3D) means that the line runs parallel to the y-axis and does not change its \( y \)-coordinate. The general form of such a line can be expressed by fixing the \( x \)- and \( z \)-coordinates, while allowing the \( y \)-coordinate to vary.

Given the point \( P\left(\frac{3}{2}, 0\right) \), the equation of the line parallel to the y-axis is:

\[
x = \frac{3}{2}, \quad z = 0
\]

The \( y \)-coordinate can take any value, so the parametric equations of the line are:

\[
x = \frac{3}{2}, \quad y = t, \quad z = 0
\]

where \( t \) is a parameter that can take any real value.

Thus, the equation of the line is:

\[
\boxed{x = \frac{3}{2}, \quad z = 0}
\]

This describes a line parallel to the y-axis, passing through the point \( \left(\frac{3}{2}, 0, 0\right) \).

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. How do you find the equation of a line parallel to the x-axis in 3D space?
2. What is the equation of a line parallel to the z-axis passing through a different point, say \( (1, 2, 3) \)?
3. How does the concept of parallel lines differ in 2D and 3D space?
4. How would you find the distance between a point and a line in 3D space?
5. What is the general form of a line equation in 3D using direction ratios?

**Tip:** When working with lines in 3D, remember that fixing two coordinates allows the third to vary, describing lines parallel to one of the axes.

Discover how to determine the equation of a line parallel to the y-axis through point P (3/2, 0) in 3D space. Learn about parametric equations and coordinate geometry concepts. Suitable for Grades 10-12 students and anyone interested in 3D geometry.

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