Calculus

posted by .

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?

  • Calculus -

    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.

  • Calculus -

    *oops (5/2,1/2,0) for position

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

  • Calculus -

    Do you know why they divided it by 2?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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=
  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 …
  3. 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 …
  4. 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?
  5. 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 exists, …
  6. 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 have …
  7. Calculus

    1. a) Write the vector and parametric equations of the line through the points A(6, -1, 5) and B(-2, -3, 6). b) Find another point on the line in (a). ----- This is what I got for a) r = 6i-j+5k + t(-8i-2j+k) x = 6-8t y = -1-2t z = …
  8. 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 …
  9. 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, …
  10. 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

More Similar Questions