I am not sure how to do this problem at all any help would be great. ? The vector equation for the line of intersection is calculated using a point on the line and the cross product of the normal vectors of the two planes. I need to parametrize the intersection between the cylinder $ x^2 + y^2= \frac{1}{4}$ and the sphere $(x+ \frac{1}{2})^2 + y^2 +z^2 = 1$. About Pricing Login GET STARTED About Pricing Login. A cast-iron solid cylinder is given by inequalities \(x^2 + y^2 \leq 1, \, 1 \leq z \leq 4\). Step-by-step math courses covering Pre-Algebra through Calculus 3 x=5cos(t) and y=5sin(t) 01-27-2015, 08:46 PM. Use sine and cosine to parametrize the intersection of the surfaces x2 + y2 = 9 and z = 5x3. Use sine and cosine to parametrize the intersection of the cylinders x^2+y^2=1 and x^2+z^2=1 (use two vector-valued functions). The vertical (xy) projection of the curve is a circle. If two planes intersect each other, the intersection will always be a line. Parameterize the curve of intersection of the cylinder x^2 + y^2 = 16 and the plane x + z = 5 Homework Equations The Attempt at a Solution i think i must first parameterize the plane x = 5t, y = 0, z = -5t then i think i plug those into the eq. The intersection of any plane with any sphere is a circle. Example: Find a parametrization of (or a set of parametric equations for) the plane \begin{align} x-2 y + 3z = 18. In most cases this plane is slanted and so your curve created by the intersection by these two planes will be an ellipse. The plane in question passes through the centre of the sphere, so C has the same centre and same radius as the sphere. Example 1Let C be the intersection of the sphere x 2+y2+z = 4 and the plane z = y. Intersection Of a Plane and Cylinder? I'm wondering if there is a way I can construct and callout a line where a cylinder meets a plane. So C has radius 2 and centre (0,0,0). We wish to parameterize the intersection of the above cylinder and the plane x+y+z=1, solving this for z gives z=1-x-y so we see that if we put Find a vector-parametric equation for intersection of the circular cylinder x^2+z^2=6 and the plane 4x+8y+5z=1. Get 1:1 help now from expert Calculus tutors Solve it with our calculus problem solver and calculator The temperature at point \((x,y,z)\) in a region containing the cylinder is \(T(x,y,z) = (x^2 + y^2)z\). Expert Answer 100% (8 ratings) Previous question Next question Get more help from Chegg. You know that in this case you have a cylinder with x^2+y^2=5^2. CALCULUS HELP!! The projection of C onto the x-y plane is the circle x^2+y^2=5^2, z=0, so we know that. ... the intersection is a single point at the xy plane. 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