What are the parametric equations of a line perpendicular to two given lines?

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To find the parametric equations of a line through point A(-3,2,5) that is perpendicular to both given lines, one must first determine the direction vectors of line 1 and line 2. The direction vector for line 1 can be extracted from its parametric form, while line 2's direction vector is derived from its equation. The next step involves calculating the cross product of these two direction vectors, which yields a normal vector that defines the perpendicular line. Once the normal vector is established, the parametric equations can be formulated using point A and the normal vector. This approach effectively solves the problem of finding the required line.
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Homework Statement



find the parametric equations of the line through A(-3,2,5) and is perpendicular to both line 1 and line 1 where

line 1: (x-4)/3=y-2=(z-3)/-2
line 2: (x,y,z)=(-1,1,5)+k(-1-2,3)


2. The attempt at a solution

i think i need to find the normal for the line 1 and line 2.. but I'm not sure.. also i have a unit test on this tomorrow.. so any help would be great
 
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You need to find tangent vectors to both line1 and line2. Can you start by doing that? Are you, by any chance, in the same test as passenger48?
 
oh i finally figured it out.. i just need to do the cross product of the two dirction vectors of the two line..
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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