Calculus

posted by .

Find the equation of the plane through (1,2,-2) that contains the line x = 2t, y = 3 - t, z = 1 +3t

  • Calculus -

    The direction vector of the given line is (2,-1,3) and a point on it is (0,3,1)
    So using that point and the additional given point (1,2,-2)
    yields a second direction vector of (1,-1,-3)

    So we need a normal to these two direction vectors, which is the cross-product of (2,-1,3) and (1,-1,-3)

    I got this normal to be (6,9,-1)
    (I will assume you know how to find the cross-product)

    The equation of the plane is
    6x + 9y - z = k
    subbing in the given point (1,2,-2)
    6 + 18 + 2 = k = 26

    equation of plane : 6x + 9y - z = 26

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    Find an equation of the plane orthogonal to the line (x,y,z)=(-4,-9,9)+t(-8,-1,5) which passes through the point (-9,9,-4). Give your answer in the form ax+by+cz=d.
  2. vector calculus

    find an equation for the plane that contains the line x = 2t-8, y=3t +3, z= 5- t, and the point (5,4,0)
  3. calculus

    find a vector equation of the line, which passes through the point (1,3,11) and is perpendicular to the yz-plane
  4. calculus

    find an equation for the line with the given properties. express the equation in slope-intercept form. containing the pointsP=(-1,1)& Q= (1,-2) What is the equation of the line?
  5. Calculus 3

    Find the equation of the plane that passes through (1,0,0) and is perpendicular to the line r=<1,0,2>+t<1,0,1>. The vector equation of a plane is n*(r-rsub0)=0. Thank you so much for your help!
  6. 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
  7. Calculus

    Find an equation of the plane. The plane that passes through (8, 0, −2)and contains the line x = 6 − 2t, y = 3 + 5t, z = 3 + 2t
  8. Calculus

    Find an equation of the plane. The plane that passes through the point (−1, 2, 1)and contains the line of intersection of the planes x + y − z = 4 and 4x − y + 5z = 4
  9. Calculus

    Consider the line through the points (3,2,5) and (1,1,1). Consider the plane A that is perpendicular to this line, and passing through the point (-1,0,2). Consider the plane B that passes through the points (1,-1,0), (0,2,0), and (0,5,2). …
  10. Calculus

    a) Find parametric equations for the line through (4, 1, 4) that is perpendicular to the plane x − y + 2z = 7. (Use the parameter t.) b) In what points does this line intersect the coordinate planes?

More Similar Questions