Plane Z 0

Determine the volume of the region that lies under the surface z 4 x 2 y 2 and above the plane z 0. Line intersect plane z 0.

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There are two ways to go at it.

Plane z 0. Because z 0 is the only restriction we can choose x and y freely. Specifically let r 0 be the position vector of some point p 0 x 0 y 0 z 0 and let n a b c be a nonzero vector. 1 you can choose two vectors in the plane and calculate the cross product.

Thus x 1 3t 10 and y 2. From the parametric equation for z we see that we must have 0 3 t which implies t 3. As 0 0 0 is in the plane choosing any two points on the plane gives you two vectors.

I can find information about a plane that is not flat. The line intersect the xy plane at the point 10 2. Thus 1 0 0 and 0 1 0 are possible vectors.

Ask question asked 3 years 11 months ago. The plane determined by the point p 0 and the vector n consists of those points p with position vector r such that the vector drawn from p 0 to p is perpendicular to n. I cant find any information about it.

A plane is determined by a point p 0 in the plane and a vector n called the. Viewed 773 times 0 begingroup if got a problem with getting the point of intersect a line throug a plane. By signing up you ll get.

Active 8 months ago. Find the volume of the solid with plane z 0 as the bottom the cylinder x 2 y 2 2 as the side and the plane z 3 x y as the. Well the line intersects the xy plane when z 0.

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