Calculus

posted by .

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?
xy-plane?
yz-plane?
xz-plane?

  • Calculus -

    the normal to the plane has direction cosines proportional to <1,-1,2>, so
    x = 4+t
    y = 1-t
    z = 4+2t

    xy-intercept:
    z=0, so t = -2
    (2,3,0)
    and so on

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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?
  2. calculus

    Find parametric equations for the line through the point P(2, 9, 4) that is parallel to the plane x + y + z = 6 and perpendicular to the line x = 5 + t , y = 5 − t , z = 5t . Answer Choices: 1. x = 2 + 6t, y = 9 + 4t, z = 4 + …
  3. Calculus grade 12

    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).
  4. 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 = …
  5. calculus

    Find parametric equations for the line that is perpendicular to the plane 2x-y+3z=7 and intersects the plane when x=1 and y=1.
  6. Calculus

    Find parametric equations for the line through the point (0,2,2)that is parallel to the plane x+y+z = 2 and perpendicular to the line x=1+t, y=2−t, z=2t. (Use the parameter t.) (x(t), y(t), z(t)) =
  7. Math

    The parametric equations for a line L1 are as follows: x = 2+2t y = 2+2t z = −3+2t Let L2 be the line parallel to L1 and passing through the point (1, −4, −3). Find the point P on L2 whose x-coordinate is −4. …
  8. math

    Let L be the line with parametric equations x = −8+2t y = 4+3t z = −4 Find the vector equation for a line that passes through the point P=(−2, 1, 3) and intersects L at a point that is distance 2 from the point Q=(−8, …
  9. vectors linear algebra

    The parametric equations for a line L1 are as follows: x = −4−6t y = 2+2t z = 1−4t Let L2 be the line parallel to L1 and passing through the point (−3, −3, −3). Find the point P on L2 whose x-coordinate …
  10. Vectors

    Show that the line with parametric equations x = 6 + 8t, y = −5 + t, z = 2 + 3t does not intersect the plane with equation 2x − y − 5z − 2 = 0.

More Similar Questions