Calculus

posted by .

Find the vector equation of the line that passes through the point (2,-1,7) and is parallel to the line of intersection of the planes x + 2y - 3z = -6 and 3x - y + 2z = 4

  • Calculus -

    We need the direction of their line of intersection....
    double the 2nd plane equation, then add that to the 1st

    x+2y-3z = -6
    6x - 2y + 4z = 8
    7x + z = 2
    z = 2-7x

    let x=1
    then z = -5
    back in the 1st
    1 + 2y + 15 = -6
    y = -11 -----------> point (1,-11,-5)

    let x = 0
    then z = 2
    back in 1st
    0+2y -6 = -6
    y = 0 ------------> point (0,0,2)

    direction vector of line of intersection of the planes = (1, -11, -7)

    so one such vector equation is
    r = (2,-1,7) + t(1,-11,-7)


    (the question should have said, "Find a vector equation...."
    since the answer I obtained is not unique)

  • Calculus -

    We need the direction of their line of intersection? That's all the question mentioned... so is that still the correct answer? :/

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Use normal vectors to determine the intersection, if any, for each of the following groups of three planes. Give a geometric interpretation in each case and the number of solutions for the corresponding linear system of equations. …
  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. 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, …
  5. Calculus

    Find the vector equation of the line that passes through the point (2,-1,7) and is parallel to the line of intersection of the planes x + 2y - 3z = -6 and 3x - y + 2z = 4
  6. precalc

    I;m not sure if i am doing this right...I keep getting a negative intersection point, which doesn't seem possible. Please help! a) find the equatoin of line 1 which passes through (1,3) and (9,7) I get y=3+1/2(x+1)or y=1/2x+2.5 b) …
  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 …
  8. Calculus Grade 12

    Find the equation of the plane that passes through the point (3,7,-1) and is perpendicular to the line of intersection of the planes x-y-2z+3=0 and 3x-2y+z+5=0
  9. MAT221

    consider the line 8x-5y=-4 find the equation of the line that is perpendicular to this line and passes through the point (-4,-4) find the equation of the line that is parallel to this line and passes through the point (-4, -4) i keep …
  10. math

    a vector parallel to the line of intersection of the planes. x-2y-z=6 and 3x-y+z=4 the answer is <3,4,-5> so first, I took the cross product of <1,-2,-1> and <3,-1,1> which I think is v. in the equation p0 + tv. << …

More Similar Questions