Perpendicular Line Equations for Skew Lines in Different Planes

[Iyafrady]

Homework Statement

Find equations for a line perpendicular to both of these lines.

Homework Equations

(x/3)=(y/2)=(z/2) and (x/5)=(y/3)=(z-4)/2

The Attempt at a Solution

i don't know how to start?I know the two lines are skew, if i take the cross product will it be perp. to both lines??Can i take the cross product of two lines that lie in different planes?

 

[Dick]

You don't take the cross product of the lines. You take the cross product of the direction vectors of the lines. The result is a direction vector for the perpendicular line.

 

[Iyafrady]

how do i find the direction vectors?

 

[Dick]

Do you have a textbook? Isn't it covered in there?

 

[Iyafrady]

No!My book leaves a lot of details out, it expects us to know certain calculus stuff since its a post calculus course.I just don't remember direction vectors but have studied them in the past.Ill see what i can find n google.thnx anyway.

 

[Dick]

Then you may need another book to keep on hand. ax=by=cz has direction vector (1/a,1/b,1/c).

 

[Iyafrady]

Hmm, i did the cross product of the direction vectors and got -2i+4J-k, but the questions asks to find the equations, i got a vector.The answer in the book is .5x-52/7=-.25y+52/21=z-208/21, they surely used another method.

 

[Dick]

No. Look at the direction vector of the line they give as a solution. It's (1/.5,1/(-.25),1/1) which is (2,-4,1). You got the direction vector right. Now it looks like they want you to fix the constants by requiring that the perpendicular intersect the other two lines.