8.) Find the planes tangent to the following surfaces indicated points: a:) x² + 2y ²2/3 X ² = 10₁ at the point (1,2,3) 2 b.j g²-x² = 3 at the point (1, 2,8). C.J xyz = 1, at the point (1,1,1). //

Q: 5. Find an equation plane to the surface (u, v) = (3 cos(u) sin(v), 2 sin(u) sin(v), cos(u)) at the…

A: First, we find the point on the surface where the tangent plane would be drawn. Next, we calculate…

Q: 2. Find the equation of the tangent plane to the surface x²+3y²+4z² = 20 (2,2, 1). at the point

A: Step 1:To find the equation of the tangent plane to the surface x2+3y2+4z2=20 at the point (2,2,1),…

Q: Find the angle between the surfaces x² + y² + z² = 41 and z = x² + y²-11 at the point (4, 0, 5):

A:

Q: = . Find an equation of the tangent plane to the parametric surface R(u, v) 0≤u≤, at the point…

A:

Q: Find the point(s) on the surface z2 = xy+1 which are closest to the point (10, 8, 0). List points as…

A: The objective is to find the points on the surface z2=xy+1 which are the closest to the point 10,8,0…

Q: The surface z = x² - y² and the surface ryz = -30 intersect along a curve in R³. Find a vector…

A:

Q: 5. Let L₁ be the line with parametric form (x, y, z) = (1, 0, 2) + (-1,2,3), and let L₂ be the line…

A: Given,The parametric form of the line ,The parametric form of the line ,.Aim: (a) To find the angle…

Q: Match each parametrization with the corresponding surface. (i) (u, cos (v), sin (v)) (iv) (u, v³, v)…

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Q: Express the following curves parametrically, including the interval for the parameter. 2.) 2.) A…

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Q: al Let fix,y) = xey². a) Find the equation for the tangent plane to the graph off at (12) b. What…

A:

Q: Which of the following is the coordinates of all points on the surface with equation z = x³-5xy¹…

A: To find the coordinates of all points on the surface where the surface has a horizontal plane, we…

Q: Find the equation of the plane tangent to the graph of z + xyz = 33 at (1,2,3).

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Q: / Find the distance from the line x 2 + 1, y 1 +1, z = -(1/2) - (1/2)t to the plane x + 2y + 6z 10.

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Q: Find equations for the a) tangent line and b) normal plane to the curve made by the intersection of…

A: Given The given surfaces are 3x2y+y2z=-2 and 2xz-x2y=3.  The given point is 1,-1,1.

Q: Find the points on the surface 1x² + 1y² + 3x² = 1 at which the tangent plane is parallel to the…

A: We know that two planes are parallel if their normal vector are parallel. That is their, gradient…

Q: Which of the following is the least distance from the point (2, –1,1) to the plane x + y – z = 2?

A: Given: The plane equation is x+y-z=2and the distance from the point is 2,-1,1 To find the least…

Q: find the distance between spheres  x2+(y-12)2+z2=1 and (x-3)2+y2+(z-4)2=9.

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Q: 2. Find a set of parametric equations for the tangent line to the curve of intersection of the…

A: Step 1:To find the parametric equations for the tangent line to the curve of intersection of the…

Q: 285. Find the scalar equation of the plane that passes through point P(-1, 2, 1) and is…

A:

Q: b) Find the angle between the surfaces x² + y² + ² = 19 and 2 = 2 x² + y²-7 at the point (3, 1, 3):

A:

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

A: Given: