(1 point) Find the angle between the plane z=0 and the plane passing through the points (0, 0, 0), (2, 3, 0), and (0, 3, 3)


Calculate the normal vectors of both planes and then use the dot product of these two vectors to calculate the angle between them. This gives you the angle between the planes.


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Nathalie Olcese
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Nathalie Olcese

Updated on July 23, 2022


  • Nathalie Olcese
    Nathalie Olcese over 1 year

    i know when I have to vectors I can get the cosine the dot product but I don't know how to proceed with this question.I think using the cross products for the points might be a good way to solve it.

  • Nathalie Olcese
    Nathalie Olcese about 6 years
    I used the cross product to find the normal vector of the second plane but im having problems with the first planes z=0 .I am assuming I and j are 1 each.
  • Attila Kinali
    Attila Kinali about 6 years
    This one is not difficult either. There are two ways to go at it: 1) You can choose two vectors in the plane and calculate the cross product. As $(0,0,0)$ is in the plane choosing any two points on the plane gives you two vectors. Because $z=0$ is the only restriction, we can choose $x$ and $y$ freely. Thus $(1,0,0)$ and $(0,1,0)$ are possible vectors. Calculate the cross product and you are done. 2) You can argue geometrically and say that if $z=0$ then the plane is the $x$-$y$-plane. Hence its normal vector points in the direction of the $z$-axis. Hence $(0,0,1)$ is a normal vector