Calculus Grade 12 University

posted by .

8. Find the vector equation of the line in which the 2 planes 2x - 5y + 3z = 12 and 3x + 4y - 3z = 6 meet.

  • Calculus Grade 12 University -

    just take the cross-product of the normals to find the direction of the vector:

    | i j k |
    | 2 -5 3 |
    | 3 4 -3 |
    = 3i+15j+23k

    Now find a point on the line:

    if x=0, y=-18,z=-26

    the line is thus

    3ti + (-18+15t)j + (-26+23t)k

  • Calculus Grade 12 University -

    thanks steve.

    do you know how to do these ones? :(

    4. Write a vector equation of the line through the point (5, -2, 3) and parallel to the vector v=[4, -3, 1]

    5. Determine an equation for the plane that is exactly between the points A(-1, 2, 4) and B(3, 1, -4).

    6. Find out if the line r = (1, 3, 8) + t (-2, 5, 7) is parallel to the plane 3x + 4y - 2z = 1

    7. Where does the line r = (1, 2, -5) + t (2, -3, 1) meet the plane 2x + 5y - 3z = 6?

  • Calculus Grade 12 University -

    for the #4 i got

    r = (5, -2, 3) + t(4, -3, 1)

    --- can you please help me on 5, 6, 7. instead since i got 4. thanks steve

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. 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, …
  3. Precalc

    A line in space has the vector equation shown here. Fill in the blanks to find the position vector to the fixed point on the line that appears in the equation: vector r=(5+(6/11)d)vector i + (3+(9/11)d)vector j + (7+(2/11)d)vector …
  4. 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
  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. 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 …
  7. maths-urgently needed

    find the vector and the cartesian equation of the line passing through (1,2,3) and parallel to the planes x-y+2z=5 and 3x+y+z=6
  8. maths-urgently needed

    find the vector and the cartesian equation of the line passing through (1,2,3) and parallel to the planes x-y+2z=5 and 3x+y+z=6
  9. 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
  10. math

    Hi I wanted to check my work for this problem. Consider the points A(1,0,0) B(2,2,2) and C(0,2,1). 1) Find the vector CA x CB I got -2i -3j +4k for this 2) Find an exact value for the area of the triangle ABC. I got sqrt29/2 for this. …

More Similar Questions