Q1: Find the parametric rquations of the line that passes through the point P(4,2,-3) and Q(-3,2,2). At what point does the line intersect the xy-plane?. 02:Determine the equation of tangent plane and normal line of the surface

Q: The surface z=f(x,y) intersects the plane x-2 along the curve C which has equation of dy Find at the…

A: Given Data: The equation of the curve is: z=13y3-y2 The point at which derivative is required is: x,…

Q: Q1) Find equation of line normal to plane 3x + 2y - z = 5 and pass through Origin point. 30 mark

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Q: = 21 which is parallel to the plane Find the equation of tangent plane to the surface x? + 2y? + 3z2…

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Q: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface.5.…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

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Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

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Q: Find the 'slope' of the tangent line to the curve of intersection of this surface 3z = 36-9x –4y?…

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Q: Solve for an equation of tangent plane and parametric and symmetric equations of normal line to the…

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Q: find parametric equations for the line tangent tothe curve of intersection of the surfaces at the…

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Q: Find an equation of the tangent plane to the surface z = -2z² – 2y?- lz 2y+ 3 at the point (5, 1,…

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Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — 3ху —у? -2…

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Q: Find the equation of tangent plane and normal lines of the surface: t the point (1,3, 2).

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Q: Write parametric equations for the tangent line to the curve of intersection of the surfaces x +y +z…

A: We know that the parametric equation of a tangent line to the curve of intersection of the two…

Q: Find equations of the Normal plane and Osculating plane of the curve y = 2t, x = 2 sin 3t , z =…

A: Consider the equation of a plane as, ax-x0+by-y0+cz-z0=0 Here, a, b, c, are the slopes in x, y, z,…

Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

A: To find a parametric equation of the line tangent to the curve of intersection of the surfaces at…

Q: Find parametric equations for the tangent line at (1, 3, 3) to the curve of intersection of the…

A: First, find the function of the surface in three variables, f(x,y,z).  f(x,y,z)=x2y-z Find the…

Q: 8. Determine the equation of the plane tangent to z point (x, у, z) 3 (-2, 1, 4). x*y3 at the =

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Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

A: Given that z=x2+y2 and 3x−5y+7z=24 and point is 3,4,5. Let fx,y,z=x2+y2−z and gx,y,z=3x−5y+7z−24 We…

Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y? = 8,…

A: Given: The parametric equations for the line tangent to curve of intersection of the surfaces…

Q: Find parametric equations for the line tangent to the curves of intersection of the surfaces xyz =1…

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Q: List all of the points (x,y on the parcmetric curve X= +?+ 4+ y= 6+3 where the tangent line is…

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Q: Find the equation of the tangent line to the parametric curve x = 2t2 and y = 7t2 – 2t3 – 1 at the…

A: find the slope of function using the chain rule and then use the equation  of a tangent line to…

Q: Find parametric equations of the normal line to the surface z = 4 + y² at the point (2, –2, 5) |

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Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x = 74…

A: given curves x2+z2=74 , y2+z2=74 , point 5,-5,7  to find parametric equations for the tangent line…

Q: Find the tangent line(s) to the parametric curve given by a = t-9t and y =t at (0, 9) %3D %3D

A: We have to find the tangent line

Q: Solve for an equation of tangent plane and parametric and symmetric equations of normal line to the…

A: Given Surface is xz + 2xy + yz = 10

Q: Find the slope of the tangent line to the curves cut from the surface z= 3x? +4y? -6 by planes…

A: The solution are next step

Q: Write parametric equations for the tangent line to the curve of intersection of the surfaces x +y +z…

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Q: 12. Find an equation for the tangent plane to the surface given by 2xy? = 2z2 – ryz at the point (2,…

A: We know that the equation of the tangent plane is: nxx-x0+nyy-y0+nzz-z0=0 Where n→-nxi+nyj+nzk is…

Q: Find the equation of tangent plane and normal lines of the surface: f(x, y, z) = 5x² + 4 y2 +z³-9 at…

A: Here we have to find the equation of the tangent plane and normal lines of the surface:…

Q: Find the equation of tangent plane and normal lines of the surface: ( x, y, z) = 5x^2 +  4y^2 + z^3…

A: We have to find the equation of tangent plane and normal lines of the surface: f(x,y,z)=5x2+…

Q: Find the equation for the tangent plane to the surface z = Vy -x at the point (2,3,1). Use a…

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Q: Find an equation of the tangent plane to the given surface at the specified point. 3Vy Z = VY, (-1,…

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Q: 4. z%3е-**-у", (1, 1, е-2)

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Q: Consider the equation of the surface S given by: exyz + x3z3 − 3y4 = 9 An equation for the plane…

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Q: Find parametric equations for the line pass- ng through the point P(1, –1, 3) and perpen- licular to…

A: Given that: Line is passing through P(1,-1,3) and perpendicular to the plane:       4x+3y-2z=6.

Q: Find the parametric equations of the tangent line to the curve of intersection of the surfaces x² -…

A: The equation of the tangent plane to the surface f(x, y, z)=0 at x0, y0, z0 is defined as: fxx0, y0,…

Q: 4. Find an equation of the tangent plane to the surface x = u? + 1, y = v + 1, z = u + v at the…

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Q: 4. Find the parametric equations for the tangent line to the curve of intersection of the y z 1…

A: Given:

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 the parametric equations of normal line to the surface given by f(x, y) = tan v x2 +y2 at the…

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Q: Find the equations of the tangent plane and normal line to the surface with equation 9y? + 9z2 = 22…

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Q: Find an equation of the tangent plane to the surface at the given point. z = 8 – (3, –4, 4)

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Q: Find set of parametric equations for the tangent line to the curve of intersection of the surfaces…

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Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

A: Given, the surfaces:               x+y2+2z=4,   x=1  Point: (1, 1, 1) Let         z = 1-2t

Q: he normal vector to the tangent plane for the surface point (1, 2, -1) is: Select one: None of them…

A: topic:- application of derivatives

Q: Write parametric equations for the tangent line to the curve of intersection of the surfaces x =…

A: To find: The parametric equations for the tangent line to the curve of the intersection of the…

Q: Find an equation of the tangent plane to the given surface at the specified point. 5Vy Z = (-1, 1,…

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Q: 2. Find an equation of the tangent plane to the parametric surface F(u, v) = (, 2uv, uv?) at the…

A: (2) Consider the provided question,