Calculus

Find the parametric equations for the line of intersection of the planes x+y+z=3 and x-y+2z=2

I took the cross product of the 2 equations and got 3i-j-2k

I then set z=0 and got x=5/2 and y=1/2.
I got:
x=5/2 +3t
y=1/2-t
z=-2t

However, the answers are supposed to be:
x=5/2-(3/2)t
y=1/2+(1/2)t
z=t

What is my procedure missing to get there?

  1. 👍 0
  2. 👎 0
  3. 👁 86
  1. I think your method is correct.
    You took the cross product of the two vectors of the plane <1,1,1>x<1,-1,2> and got the direction vector v=<3,-1,-2>

    You combined the two equations and got (0,5/2,1/2), which gives you the position


    There are many different solutions for an equation of a line. So don't think that your answer is wrong.

    1. 👍 0
    2. 👎 0
    posted by A.
  2. *oops (5/2,1/2,0) for position

    Looking at the answer again,
    it looks like they divided the vector by 2

    1. 👍 0
    2. 👎 0
    posted by A.
  3. Do you know why they divided it by 2?

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Vectors

    3 planes; $: x+2y-2z-6=0 %: 2x-y+z+8=0 £: 2x-y+2z+3=0 (a)(i)Find the cartesian equation for the plane @ parallel to $ and containing the point (1,1,2) (ii)Calculate the distance between $ and @ (b)(i)Find the parametric equations

    asked by Anonymous on April 25, 2010
  2. vectors

    3 planes; $: x+2y-2z-6=0 %: 2x-y+z+8=0 £: 2x-y+2z+3=0 (a)(i)Find the cartesian equation for the plane @ parallel to $ and containing the point (1,1,2) (ii)Calculate the distance between $ and @ (b)(i)Find the parametric equations

    asked by Anonymous on April 25, 2010
  3. Calculus

    Consider the following planes. 5x − 4y + z = 1, 4x + y − 5z = 5 a) Find parametric equations for the line of intersection of the planes. b) Find the angle between the planes

    asked by Anon on September 5, 2016
  4. Math

    Find parametric equations and symmetric equations for the line of intersection of the given planes. x + y + z = 2, x + z = 0 X=1 y = Z= x=, y=

    asked by Mike on April 13, 2010
  5. Calculus

    Find the parametric equations for the line of intersection of the planes x+y+z=3 and x-y+2z=2 I took the cross product of the 2 equations and got 3i-j-2k I then set z=0 and got x=5/2 and y=1/2. I got: x=5/2 +3t y=1/2-t z=-2t

    asked by Mackenzie on December 4, 2012
  6. maths - geometry

    In a space with an orthonormal coordinate system consider the plane; &: 4x-3y=12 (a)(i)Find the coordinates of the points of intersection of the plane & with the coordinates axes (=axes intersections???) (ii)Find the parametric

    asked by Anonymous on April 28, 2010
  7. Calculus

    Consider the planes given by the equations 2y−2x−z=2 x−2y+3z=7 (a) Find a vector v parallel to the line of intersection of the planes. (b)Find the equation of a plane through the origin which is perpendicular to the line of

    asked by Felicia on October 1, 2012
  8. Vectors

    which is not a possible type of intersection between three planes? a) intersection at a point b) three coincident planes c) intersection along a line d) intersection along a line segment I know that planes can intersect in a line

    asked by Sara on March 11, 2015
  9. Math - intersection of planes

    You are given the following two planes: x+4y-3z-12=0 x+6y-2z-22=0 a) Determine if the planes are parallel b) Fine the line of intersection of the two planes. c) Use the two original equations to determine two other equations that

    asked by Shaila on September 4, 2010
  10. Math - Intersection of planes

    Find the vector equation of the line of intersection for the pair of planes. Plane one: x+5y-3z-8=0 Plane two: y+2z-4=0 I did half of the work but now i am stuck. the normal of the planes are not parallel and therefore a solution

    asked by Shaila on September 1, 2010

More Similar Questions