Check that the point (1, -1, 2) lies on the given surface. Then, viewing the surface as a level surface for a function f(x, y, z), find a vector normal to the surface and an equation for the tangent plane to the surface at (1, –1, 2). 3x? – 3y2 + 3z? = 12 - vector normal = tangent plane:

Q: a) Start by finding a single vector function that represents the intersection of the surfaces z =…

A: (a) Given that: Start by finding a single vector function that represents the intersection of the…

Q: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface.3.…

A: To find equations for the(a) tangent plane and(b) normal line at the point P on the given surface.…

Q: Find parametric equations of the normal line to the surface z = 4 +y? at the point (2, 3, 10) O x =…

A: To Find:  the parametric equations of the normal line to the surface  z = x24+y2 at the point ( 2,…

Q: (a) Find equation of the tangent plane and normal line to the sphere x? + y? + z? = 25 at the point…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. x² + y2 + z2 = 26, (1,…

A: Given problem:- (a) Find an equation of the tangent plane to the surface at the given point.   x2 +…

Q: Given w f(z,y, 2) = zy²z. Find: Ograd/(1,3,-2) 3. (b) equation of the tangent plane to the surface…

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Q: A surface z = f(x, y) is defined implicitly by the equation x +y+ z – e² = 3 – e. - Determine the…

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Q: Consider The curve of intersection of the parabolic cylinders x = y? and z = x?. Find an equation of…

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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: Find the equations of the normal line and the tangent plane to the parametric surface defined by the…

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Q: Consider the ellipsoid 3x? + y? + z² = 11. The equation of the tangent plane to this ellipsoid at…

A: 3 x2 + y2+z2=11 and the point is (1,-2,-2)

Q: Find the equation of the tangent plane to the surface 2² at the point Y= 2x? (0, –1,2) %3D O y- 2z…

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Q: The vector (x, 2y, –3z) is normal to the surface x2 + 2y? – 32 – 4 = 0 at any point (x, y, z). - - -

A: Let's find.

Q: Find the tangent plane and normal line of the level surface ƒ(x, y, z) = x2 + y2 + z - 9 = 0 at the…

A: Given ƒ(x, y, z) = x2 + y2 + z - 9 = 0

Q: Find an equation for the plane that is tangent to the surface z= Vy - I at the point (2, 3, 1).

A: We have to find partial derivatives first.

Q: The equation z = f(x,y) = y +x -3y defines a surface. What is t- equation of the tangent plane at…

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Q: Find an equation of the tangent plane to the surface represented by the vector-valued function at…

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Q: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given surface x*…

A: According to bartleby guidelines when student asks more than one question expert have to answer…

Q: Find the slope of the tangent line at (-1, 1,5) to the curve of intersection of the surface z = x²…

A: According to question, we have, z = x2 + 4y2        .......(1)

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 an Equation for the tangent plane and normal line at the points Po on the given surface. x +…

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Q: Find the equation of the tangent plane for the surface z = xy at the point (-1,2,-2) O z=x-2y+2…

A: The equation of tangent plane for the surface z =f(x,y ) at point (m,n,f(m,n)) is given as:

Q: A normal vector to the tangent plane for the surface a y"z* = 1 at the point (1, 1, –1) is: %3D…

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Q: Write an equation for the plane tangent to the surface F(x, y, z) = 0 at the point (a, b, c).

A: Given surface is Fx, y, z=0 and the point is a, b, c.

Q: (a) Find equation of the tangent plane and normal line to the sphere x + y +z = 25 at the point…

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface. 2z…

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Q: Let P be the point (2, -1, 2) and Ø,: x² + y² – z² = 10. (i) Find the unit normal vector to the…

A: (c) The given surface is ∅1: x2+y2-z2=10 and the point P: 2,-1,2. (i) The unit normal vector to the…

Q: find an equation for the plane tangent to thesurface z = ƒ(x, y) at the given point. z = 1/ (x2 +…

A: Concept - Equation of plane is given by - Ax-x0+By-y0+Cz-z0 = 0         ...............(1)where,x0,…

Q: Find the equation of the plane tangent Z= x2+ Y2 at point P (1,2,5) to the surface

A: Equation of tangent plane on the surface z=f(x,y)  at the point (a,b,c)  is given…

Q: Choose the normal vector of the tangent plane to the surface defined by z =e4x²+16xy-9y2 at the…

A: Explanation of the answer is as follows

Q: Consider the level surface defined by the equation x² - y² + z² - 4xyz = 6, find the following: a)…

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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: Find an equation of the plane tangent to the following surface at the given points. z= e*y; (6,0,1)…

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Q: Choose the normal vector of the tangent plane to the surface defined by at the point (-4, 2, e88). O…

A: Given problem:- Find the normal vector of the tangent plane to the surface defined by…

Q: Which of the following is a normal vector to the tangent plane to the surface defined by f(x, y) =…

A: To determine a normal vector to the tangent plane to the surface defined by f(x,y)=10-x2-y2 at the…

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

A: Given vector rt=2sin3t,2t,-2cos3t. Then r't=6cos3t,2,6sin3t. The given point is 0,π,-2. Now the…

Q: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given surface 1)…

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Q: Find a unit normal vector to the surface f(x, y, z) 0 at the point P(4, – 5, – 5) for the function…

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Q: Find an equation for the tangent plane and parametric equations for the normal line to the surface…

A: Let the equation of the surface be, fx,y,z=x2-xyz-165 Consider that fx, fy, and fz denote the…

Q: What is the perpendicular vector to the surface f(x.y.a)-ay-3r+'y-0 at (1,-1,2)? (3,3.0) (1,1.3)…

A: A vector that makes an angle of 90 degrees with the given surface is said to be perpendicular to the…

Q: A vector normal to the surface y-:-3 at the point (-1,-2, 2) is (a) i+2j+k (b)-i+j+2k) (e) (21 -j+k)…

A: The given surface is: xy-z=3 And, the given point is: -1, -2, 2 Since, the gradient represents a…

Q: Find a vector normal to the surface x2 + y2 − z = 0 at the point (3, 4, 25). Find the equations of…

A: Given: The equation of the surface x2+y2-z=0 at the point (3,4,25)

Q: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface. x2…

A: Consider the function fx,y,z=x2+y2-z2-18. ∇fx,y,z=fx, fy, fz=2x, 2y, -2z. At 3, 5, -4, ∇f3, 5,…

Q: Find an equation of the tangent plane to the surface z=−1x^2+1y^2+3x−1y+3 at the point (5, 5, 13).…

A: Given the equation of surface is:                               z=-x2+y2+3x-y+3 We nee to find the…

Q: Find an equation for the tangent plane and the normal line to the surface x? + 2y? – 3z² = 3, at the…

A:

Q: (a) Find equation of the tangent plane and normal line to the sphere x? + y? +z? = 25 at the point…

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Find the equation of the plane tangent of Z= x2+ Y2 to the surface at point P(42 5)

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Q: Find the tangent plane and normal line of the surface x+y+z=1 at the point p(0,1,0).

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Q: Determine the equation of the tangent plane and normal line to the surface at the given point.…

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