# Parametric Equation of Perpendicular Line Through Point of Intersection L1/L2

• yazz912
In summary, the problem is to determine the parametric equations of a line that is perpendicular to two given lines, L1 and L2, in three dimensions and passes through their point of intersection. The equations for parametric lines are x=x_1+at, y=y_1+bt, and z=z_1+ct. The first step is to find the point of intersection of L1 and L2, which can be done by solving a system of equations. To find a vector that is perpendicular to two given vectors, the cross product can be used. This should be done for both L1 and L2.
yazz912
1. The problem statement, all variables and given/known

Determine parametric equations of the line that Is perpendicular to the lines L1= 3t-2
2t
3t

L2= s-1
2s-7
3s-12

And passes through the point of intersection of lines L1 and L2

2. Homework Equations Parametric equation format:
x= x_1 +at
y= y_1 +bt
z= z_1 +ct

3. The Attempt at a Solution

We'll I'm given 2 sets of lines, I know that for something to be perpendicular I have to have the negative reciprocal of the slope.

But should my first step be to find the point of intersection of L1 and L2? Would I do this by solving a system of equations?

yazz912 said:
1. The problem statement, all variables and given/known

Determine parametric equations of the line that Is perpendicular to the lines L1= 3t-2
2t
3t

L2= s-1
2s-7
3s-12

And passes through the point of intersection of lines L1 and L2

2. Homework Equations

Parametric equation format:
x= x_1 +at
y= y_1 +bt
z= z_1 +ct

3. The Attempt at a Solution

We'll I'm given 2 sets of lines, I know that for something to be perpendicular I have to have the negative reciprocal of the slope.
Keep in mind that the lines are in three dimensions. If you have two vectors in space, a third vector that is perpendicular to the first two vectors can be obtained from the cross product.
yazz912 said:
But should my first step be to find the point of intersection of L1 and L2? Would I do this by solving a system of equations?

yazz912 said:

Im sorry do you Mind elaborating a little bit more for me?
So does that mean I can choose any two vectors from those three lines and just cross? Do this for both L1 and L2?

## 1. What is a parametric equation?

A parametric equation is a set of equations that defines a relationship between multiple variables. In the context of a perpendicular line, a parametric equation can be used to describe the coordinates of points on the line in terms of one or more parameters.

## 2. How do you find the parametric equation of a perpendicular line?

The parametric equation of a perpendicular line can be found by using the slope of the original line and the coordinates of the point of intersection between the two lines. The slope of the perpendicular line will be the negative reciprocal of the original line's slope, and the coordinates of the point of intersection will be used to determine the values of the parameters in the equation.

## 3. What is the significance of the point of intersection in the parametric equation?

The point of intersection between two lines is where they intersect or cross each other. In the context of a parametric equation for a perpendicular line, the coordinates of the point of intersection are used to determine the values of the parameters in the equation.

## 4. Can a parametric equation be used to describe any type of line?

Yes, a parametric equation can be used to describe any type of line, including perpendicular lines. However, the specific parameters and equations used will vary depending on the type of line and the given information.

## 5. How can parametric equations be useful in real-world applications?

Parametric equations are useful in many real-world applications, such as physics, engineering, and computer graphics. They can be used to model motion, describe the path of an object, and create visual representations of mathematical concepts. In the context of perpendicular lines, parametric equations can be used to determine the equations of lines that intersect at right angles, which can be useful in constructing buildings, designing bridges, and other geometric applications.

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