Find a Vector Function That Represents the Curve of Intersection

I parameterized the plane and put it into vector form. Find a vector function that represents the curve of intersection of the two surfaces.

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R t 2 cos t i 2 sin t j 5 t k 0 t π See answers 1 asked 2021-08-20 Determine whether the lines L1 and L2 are parallel skew or intersecting.

. The tangent you are looking for is perpendicular to the two tangents to the curves so the cross product will lead to a vector pointing in the direction you are looking for up to a multiplicative constant for example if you remove the 2 in the gradient vectors and operate you will get a different vector but the direction is the same. Find a vector function that represents the curve of intersection of the two surfaces. And plug that in the equation and the one we just got for z.

Find a vector function that represents the curve of intersection of the paraboloid z7x25y2 and the cylinder y5x2. Check out a sample QA here See Solution star_border. Find a vector function that represents the curve of intersection of the two surfaces.

Find a vector function that represents the curve of intersection of the two surfaces. Find a vector function that represents the curve of intersection of the paraboloid z 9x2 4y2 and the cylinder y3x2. Find step-by-step Calculus solutions and your answer to the following textbook question.

The paraboloid z 4x2 y2 The parabolic cylinder y x2 Homework Equations z 4x2 y2 y x2 The Attempt at a Solution Combining the two equations. Find a vector function rt that represents the curve of intersection of the two surfaces. Check out a sample QA here See Solution Want to see the full answer.

Y t 1 z t. Use the variable t for the. Find the curves unit tangent vector.

Find a vector function r t that represents the curve of intersection of the two surfaces. The cylinder x2 y2 16 and the surface z xy rt The cylinder x2 y2 16 and the surface z xy rt. Find a vector function that represents the curve of intersection of the paraboloid z7x2 4y2 and the cylinder y4x2.

B 10 pts Let Cbe the smooth curve parameterized by the vector-valued function. Let y t z 4t t2 Therefore. If they intersect find the point of intersection.

The cylinder x2 y2 16 and the surface z xy Advertisement Answer Expert Verified 50 5 2 MrRoyal A vector function r t is represented as. Find a vector function that represents the curve of intersection of the two surfaces. Use the variable t for the parameter.

The cone z x 2 y 2 and the plane z 1 y. The hyperboloid z x 2 y 2 and the cylinder x 2 y 2 1. X 1 y 1 1 z 2 3.

Find a vector function r t that represents the curve of intersection of the two surfaces. Also find the length of the indicated portion of the curve. Find step-by-step solutions and your answer to the following textbook question.

Zx2y212 and the plane z1y. Find a vector function that represents the curve of intersection of the paraboloid z 9x2 4y2 and the cylinder y3x2. Find a vector-valued function rt that represents the curve of intersection of the surfaces z x 2 4y2 and y x.

Since Im finding the intersection I can just plug the parameters from the plane into the cone and get x. Z 1 t 1 z t. Use the variable t for the parameter.

Therefore the vector function that represents the curve of intersection is. Paraboloid z4x2y2 and the Parabolic cylinder yx2In this case the curve o. Z 4sqrty2 y2 z 4y y2 Choose a parameter.

The vector function r t that represents the intersection of the two surfaces is Given Express 16 as in. T 1 y y t 1. We have ydetermined by xand zdetermined by xand y so we can just use rt htt 2t 4t4i.

The paraboloid z4x2y2 and the parabolic cylinder yx2. The hyperboloid z x2 - y2 and the cylinder x2 y2 1. So that we get.

Rtt Use the variable t for the parameter. T x 2 t 1 2 t 2 x 2 t 2 2 t 1 x 2 2 t 1 x 2 t 1. Use the variable t for the parameter.

R t t Expert Solution Want to see the full answer. First plug the equation of y into the equation of z so that we get their intersection. X sqrtt.

The top figure shows how the plane and the cylinder intersect and the bottom figure shows the curve of intersection C which is an ellipse The projection of C onto the xy-plane is the circle x2 y2 z 0 So we know from this example. The vector function r t that represents the intersection of the two surfaces is Given Let. Here we find a vector function for the curve of intersection of two surfaces.

The paraboloid z 7x2 y2 and the parabolic cylinder y 3x2 Advertisement Answer Expert Verified 2 MrRoyal A vector function r t is represented as. Find a vector function that represents the curve of intersection of the cylinder x2 y2 9 and the plane 4y z 13.

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