SOLUTION: line L1 and L2 has equation (x-3)/2 = (y-4)/-1 = (z+1)/1 and (x-5)/4 = (y-1)/3 = (z-1)/2. find Cartesian equation of the plane P which contain L1 and parallel to L2. L3 pass throug

Algebra.Com
Question 1134088: line L1 and L2 has equation (x-3)/2 = (y-4)/-1 = (z+1)/1 and (x-5)/4 = (y-1)/3 = (z-1)/2. find Cartesian equation of the plane P which contain L1 and parallel to L2. L3 pass through point A(-3,-2,-1) and meets P at B(-1,2,1). find Cartesian equation of L3 and acute angle between P and L3 (in nearest degree). Another line L4 with Cartesian equation (x-2)/1 = (y+3)/2 = (z+2)/1 pass through plane P. find intersection point.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
L1:
L2:
L1 is parallel to the vector < 2,-1,1 > and passes thru (3,4,-1)
L2 is parallel to the vector < 4,3,2 > and passes thru (5,1,1)
find Cartesian equation of the plane P which contain L1 and parallel to L2. 
A vector perpendicular to both those lines will be perpendicular (normal) to the
desired plane.

So we find a vector perpendicular to both vectors by crossing them:

< 2,-1,1 > × < 4,3,2 > =
 = 
< -5,0,10 >

So we want a plane containing the point (5,1,1) and having normal vector
< -5,0,10 >, which is

-5(x - 5)+0(y - 1)+10(z - 1) = 0
-5x + 25 + 10z - 10 = 0
-5x + 10z + 15 = 0
Divide through by -5
x - 2z - 3 = 0
x - 2z = 3

---------------------------------
 
L3 pass through point A(-3,-2,-1) and meets P at B(-1,2,1). 
Find Cartesian equation of L3 

-----------------------
I have to stop here because something is wrong because B(-1,2,1) is not
on plane P because substituting B(-1,2,1) into

     x - 2z = 3
(-1) - 2(1) = 3
       -1-2 = 3 
         -3 = 3 is false. 

Could it be that B(-1,2,1) could have supposed to have been B(1,2,-1)?

Check everything again.  If you answer below, I'll get back to you 
by email.

Edwin
RELATED QUESTIONS

Find the equation of the plane containing the line L1, and parallel to the line L2,... (answered by venugopalramana)
can you help me answer this :) Given; L1: 2x+4y-8=0 and L2: 2x+3y-16=0 A. Find the... (answered by josgarithmetic)
) Consider the line L in R^3 , given by x = −λ + 2, y = 2λ − 1,... (answered by ikleyn)
Consider the line L in R^3 , given by x = −λ + 2, y = 2λ − 1, and... (answered by ikleyn)
Two lines have equations L1 :[x,y,z] = [1,3,2] + t[3,0,-1] L2 :[x,y,z] = [3,1,-2] +... (answered by Edwin McCravy)
let: L1: y=3 and L2: x=3 prove that:slop(L1) × slop(L2) = - 1 (answered by MathLover1,greenestamps)
find y in the equation 1/y = 1/x + 1/z x=3, and... (answered by edjones)
1/x + 2/y - 4/z = 1 2/x + 3/y + 8/z = 0 -1/x + 9/y + 10/z = 5 then solve x, y and... (answered by Fombitz)
Please help me solve this: The equation of line l1 is 2y−5x−1 = 0. Line l2 is... (answered by josgarithmetic)