1. A

    Planes and Lines I

    There are four problems I need to know how to solve before an exam and I just can't. I was hoping that I could get some help here! Question 1: A point is mirrored in the line 4x + 3y = 0. The position of the mirrored point is (-5, 3). What is the position of the original point?
  2. J


    Sketch a graph in the xyz-space and identify the plane as parallel to the xy-plane, xz-pane, or yz-plane and sketch a graph. a) y = 4 b) x = -2 ------------------ I don't understand why the answer for (a) is plane parallel to xz-plane!
  3. O

    Please help me decide an equation for a plane

    Decide an equation in general form for a plane that is parallel to the vectors u and v and goes thru the point P=(1, 0, 3). Vectors: u=(1, -2, 0) v=(3, -5, 1) --- If the terminology is incorrect it is because I have tried to translate it from Swedish: "Ange, på normalform, en ekvation för det...
  4. X

    volume bounded sides by plane (x^2) + (y^2) +(z^2) =4 , above by sqrt ( x^2 + y^2 )

    By using spherical coordinates , find the volume bounded sides by plane (x^2) + (y^2) +(z^2) =4 , above by sqrt ( x^2 + y^2 ) , below by plane z = 0 ... Calculus III - Spherical Coordinates I'm having problem finding my Φ .... Here's my diagram ... The shaded part represent the volume...
  5. X

    surface portion bounded by plane 2x +5y + z = 10 that lies in cylinder (x^2) +(y^2)

    Find the surface portion bounded by plane 2x +5y + z = 10 that lies in cylinder (x^2) +(y^2) = 9 ... I have skteched out the diagram and my ans is 5sqrt(30) instead of 9sqrt (30) as given by the author ... Anything wrong with my working ?
  6. H

    A line and a point not on the the line lies in one plane?

    It is given that "a line and a point not on the the line lies in one plane." Why can't the point not on the line lie in another plane?
  7. X

    finding surface area using projection of plane

    by using double integrals , find the surface area (x^2) +(y^2) +(z^2) =4 that lies between plane z =1 and xy -plane why the surface area is only the ring part where the limit is sqrt rt 3 to 2 , why not the whole thong , namely from 0 to 2 ? (refer to the projection region on xy-plane)
  8. B

    Plotting in Complex Plane

    Hi, Can anyone give me some tips about plotting a quadratic and a fourth root in the complex plane. The quadratic is: z^2+2iz+1=0 The other: z^4=16 Thanks Beetle
  9. M

    Points horizontal to tangent plane - Clac 4

    Given the surface X2+Y2/9+Z2/9=1 Find the equation of the tangent plane with the points (1/3,2,2) In doing this I found the tangent plane to be Z=-1.5x-y+4.5 The question then asks for you to find a point at which the tangent plane to this surface is horizontal and if there are any such points...
  10. A

    4 points in a plane 3D

    I want to know how to find that given 4 points that they are in a plane (3D) There are 4 points with coordinates (3D) x1,y1,z1 =0,0,1 x2,y2,z2 = 0,1,2 x3,y3,z3 = 0,1,3 x,y,z = 1,0,0 One can see that the 4 points are not in a plane but I want to know the formulas to see for other points...
  11. V

    Plane Separation Postulate Help

    We learned about half plane geometry today and I am having a hard time with this proof. Any help is appreciated.
  12. T

    Checking if a point is on a plane

    So Im given 3 points that define a plane: A=(2, 1,3) B=(-1,4,1) O=(0,0,0) And am asked if the point p=(1, - 1,2) is on the same plane. I reached the conclusion it isn't. I wonder if you can understand anything from that pic... I intended to edit it but tapatalk doesn't let me before/after...
  13. S

    Find the equation of the plane given a point and two planes

    I've done a question similar to this, however this one has no complete equations i can solve for. Determine the equation of the plane that passes through (1,3,8)(1,3,8) and is perpendicular to the line of intersection of the planes 3x−2z+1=03x−2z+1=0 and 4x+3y+7=04x+3y+7=0. I know to take the...
  14. S

    Construct A Plane From A Coordinate And A Unit Vector And Find Its X,Y,Z Angles

    I'm trying to learn how to figure out the X,Y,Z rotation angles of a plane so that it is normal to a unit vector. I have a coordinate point that is on the plane and a unit vector that is normal to plane to start with. Appreciate any help I can get.
  15. M

    Vector problem: Ball bounces off a plane.

    Hey guys. I've been agonising over this problem for a while now. Can't quite seem to make sense of how to solve it, despite knowing that's it's probably fairly simple to do. Here it is: A ball is sent from point 2,6,5 in a direction so that it bounces against the plane with equation x-z=-2...
  16. K

    What is a line in R^3 and a plane in R^3?

    I am very confused on how to determine when it is a line or a a plane. Can someone explain this to me? Thank you Edit I have two problems. If A= (didnt know how to put it in a matrix (3x3) |1 3 -5| |1 4 -8| |-3 -7 9| then which best describes the kernel of A geometrically? the answer is A...
  17. C

    Volume of solid in first octant

    Find the volume of the solid in the first octant bounded by the parabolic cylinder z = 25 − x2 and the plane y = 2. I already solved it and got 710/3 as my answer, I just wanted to make sure its the right answer
  18. T

    Complex Plane Argument

    Is my sketch correct and how do I find the point on the tangent of the circle to answer question iii?
  19. B

    Distance between a point and a plane

    Find the distance between the point P1 ≡ (x1, y1, z1) and the plane through P0 ≡(x0, y0, z0) parallel to the vectors a ≡ (a1, a2, a3) and b ≡ (b1, b2, b3), where all datais given in cartesian form. Derive a general vector formula first, illustrating yourderivation with clean sketches, then write...
  20. Jason76

    Plane Equation - 5

    Solving the x,y,z equations for trespectively: x = 5t x/5 = t y = 2 + t y - 2 = t z = 3 - t -z + 3 = t Plane equation would be \dfrac{1}{5}(x - 2)+(y - 3) - (z - 5) = 0 ??