) Find a vector parametric equation for the ellipse that lies on the plane z - (4x + 3y) = -2 and inside the cylinder x2 + y² = 25. r(u, v) = →> (b) dA= F x T₂ = (c) dA= |dA|| = ||₁ × 7₂ || = for 0u5 and 0 << 2TT. (d) Set up and evaluate a double integral for the surface area of the ellipse. Surface area =

Q: how was it determined that the equation of the yz plane is x = 0?

A: The objective is to explain yz-plane equals .

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: Find the parametric equations for the line through the point of intersection of the lines L,:x = 2…

A:

Q: Find a parametric form for the line through the point (8, –6, –3) and perpendicular to the plane 2x…

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Q: The vector parametric equation for the line through the points (-3, 5, −4) and (5, −5, 0) is L(t) =

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Q: Find a set of parametric equations for the curve of intersection of the cylinder (x - 1)2 + y2/4 = 1…

A: Given: The equation of cylinder is: x-12+y24=1 .....(1) The equation of paraboloid is: x2+y-22=z…

Q: (a) Find a vector parametric equation for the ellipse that lies on the plane x + 3y + z = 5 and…

A:

Q: Find the equation of the plane passing through the point P(2, -1, 3) and perpendicular to the line…

A: We have to find the equation of the plane passing through the point  and perpendicular to the line…

Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

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Q: 7. Find the scalar equation of any plane which contains the line = (1,2,1)+ t(3,6,-1)

A:

Q: Derive the parametric equations of the line of intersection of the two planes: II : 2x – y + 2z = -1…

A: We need to find the vector equation of the line of intersection. In order to get it, we’ll need to…