Suppose F(x, y) = (5x +5y,2x + 3y) and C is the circle of radius 9 centered at the origin oriented counterclockwise. (a) Find a vector parametric equation r(t) for the circle C that starts at the point (9,0) and travels around the circle once counterclockwise for 0

Q: 5. (a) (b) The surfaces (x - 2)² + z² = 9 and y = z² intersect along the curve C. Find a vector…

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Q: Calculate the distance from point A(1, 2, 1) to the plane of equation 3x-4y + 5z = 1.

A: To find distance of point to plane using the formulae: Given point is and plane equation is .

Q: Q2/ Find the Parametric aned standand equatior of the line Hhat passer through Points (-2,1,0)…

A: The equation of line passing through given two points is given as follows:

Q: equations

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Q: Solution r(t) = 6 cos(t) i + 6 sin(t)j + 3tk. The parametric equations for this curve are x= y = 6…

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Q: Find the distance from the point Q = (1, -3, 3) to the plane 2x + 2y + 5z = 2.

A: The equation of the plane is 2x+2y+5z=2Here we have to find the distance between the plane and the…

Q: Consider the surface S of equation 2 = x² + y*" An equation for the tangent line tangent to S at…

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Q: Find the equation to the conicoid generated by lines parallel to the plane XOY, intersect OZ and the…

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Q: Suppose F(x, y) = x² + y²j and C is the line segment segment from point P = (-3,-4) to Q = (-3, 1).…

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Q: A parametric equation of a line in R³ through the point (ro, yo, Zo) and parallel to another line…

A: As we given that equation of the line passing through the point (x0,y0,z0) and parallel to another…

Q: Find the points (x, y) on the curve with the parametric equations (x3Dt3- 4t at ly=t +2 which the…

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Q: Find parametric equations for the line in which the planes x + 2y + z = 1 and x - y + 2z =-8…

A: x + 2y + z = 1 and x - y + 2z =-8 are the two planes.Let z=t So, the equations become: