Parametric Equation of Perpendicular Line Through Point of Intersection L1/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]

 

[Mark44]

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.

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?

View attachment 67095

 

[yazz912]

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?