In Exercises 7-10, calculate Tu, Tv, and N(u, v) for the parametrized sur- face at the given point. Then find the equation of the tangent plane to the surface at that point. 7. G(u, v) = (2u + v, u - 4v, 3u); u = 1, v = 4

Q: Let P be the point (1, 1, 4). Find the parametric equations of the line through P and parallel to…

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Q: Write the parametric equation of the bilinear surface corresponding to four points P(0 0)= 0.25 0…

A: Given coordinates are, P0,0=0.25,0P1,0=0.75,0P0,1=0.75,0.9P1,1=0.25,0.8 So, the parametric equation…

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: A bee starts at the point (5, 7, -3) (with units in meters) and travels at a constant speed of 9 m/s…

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Q: Let L₁ be the line parametrized by (4-2t, 2-t, 3+t). Let L₂ be the line parallel to L₁ going through…

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Q: Let C be the upper half of the circle whose equation is x2 + (y - 2)2 that is generated by revolving…

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Q: Parametrize the line segment joining the points P(1, 2, 0) and Q(1, 3, -1).

A: We know that equation of line passing through the points (x1,y1,z1) and (x2,y2,z2) is

Q: Determine the parametric equations of the curve of intersection of the paraboloid x? – y? + z² = 0…

A: Detailed explanation mentioned below

Q: Find an equation for the plane tangent to the level surface x² + y? +z = 4 at the point Po(1,1, 2).…

A: Solving

Q: 3. Determine vector and parametric equations for the plane through the point (1, -2, 3) and parallel…

A: Here we are given a point and perpendicular direction. We will express equation of plane in vector…

Q: Find the parametric equation of the intersection of the planes x + y = 1 and x + z = 2.

A: Equation of plane 1 - x+y = 1        Normal vector of plane 1 = n1 = 1,1,0…