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). 2а2 — 3у? + 422 %3D15 - 3y + 422 = 15

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: Find a vector normal to the plane with the given equation. 3(x – 5) – 5(y – 1) + 10z = 0 n =

A: Consider the equation of the plane passing through a general point Po and with normal vector n.

Q: ) Find a vector parallel to the line of intersection of the planes −4x − 2y + z = −7 and  5x +2y −…

A: (a) Given planes are −4x−2y+z=−7 and 5x+2y−5z=12 We have to find the vector v→ parallel to the line…

Q: Find a vector function r(t) that describes the curve of intersection be- tween the elliptical…

A: Given To find a vector function r(t) that describes the curve of intersection between the elliptical…

Q: The vector equation for the curve of intersection of the surfaces a = y? and z = y in terms of the…

A:

Q: Check that the point (1, –1,2) lies on the given surface. Then, viewing the surface as a level…

A:

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

A:

Q: Find a unit vector n that is normal to the surface 4z? – 2x* – 3y = 14 at P = (1,2, 4) that points…

A: To Determine: Find the unit normal n that is normal to the surface at p(1,2,4) that points in the…

Q: Check that the point (−1,−1,1) lies on the given surface. Then, viewing the surface as a level…

A:

Q: Check that the point (1, 1, 1) lies on the given surface. Then, viewing the surface as a level…

A: Folow 2nd and 3rd step we find out vector normal and tangent plane of given surface at given point.

Q: Find the equation of the tangent plane to the surface =1 16 at the point (1,-3,2) O a. 3x-2y+z=24 O…

A: Given: x24+y29+z216=1 x,y,z=1,-3,2. Simplify the equation.…

Q: Find a vector equation with parameter t for the line of intersection of the planes x + y + z = 4 and…

A: To find the equation of line with parameter t of the intersection of the planes  x + y + z =4 and…

Q: Find a vector parallel to the line of intersection of the planes 5x−y+2z=4 and 4x−y−3z=0v→=  (b)…

A: Find a vector parallel to the line of intersection of the planes 5x−y+2z=4 and 4x−y−3z=0

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: Given two surfaces Z =   x2 + y2  and  plane z = 9 + y  We have to find vector function   r (t) We…

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: Find the normal vector to the surface z = xe™Y at the point (2,0, 2).

A:

Q: Find the equation oftangent plane and normal lines ofthe surface: f(x,y, z) = 10x² –14 y² +11z³-7 at…

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Q: Find a vector equation with parameter t for the line of intersection of the planes x + y + z = 3 and…

A: Given plane equations are  x + y + z = 3 and x + z = 0. We have to find the intersection line…

Q: Determine the vector equation that represents the curve of intersection between the cylinder 2¹² +…

A:

Q: Sketch the curve associated with the vector function r(t) = . Hint: Show it lies on the surface z?…

A: Given the vector function is r→t=tcost,tsint,t. Skecth the curve associated with the above vector…

Q: Find a vector function r(t) that describes the curve of intersection between the elliptical cylinder…

A: given, elliptical cylinder 4y2+z2=4  and the plane x+y=1 we have to find a vector function r(t) that…

Q: The cone z = x² + y² and the plane z = 1 + y

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Q: Find a vector function that represents the curve of intersection of the cylinder x^2 +y^2 =1 and the…

A:

Q: Find a vector normal to the plane with the given equation.3(x − 4) − 8(y − 1) + 11z = 0

A: Consider the equation of the plane: 3x-4-8y-1+11z=0.   If equation of the plane has the form:…

Q: Let S be the surface described by the vector function Ř(u, v) = (v², u + v, e²«). Find an equation…

A:

Q: Find the Vector function that represents the curve of the intersection of the two surfaces.  The…

A: Given equations are x2+y2+4z2=4 ..... (1) and x2+z2=1 ..... (2) From equation (1) z2=(4-x2-y2)/4…

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

A:

Q: Find the equation oftangent plane and normal lines of the surface: ƒ(x, y, z) = 10x² –14 y² +11z³-7…

A:

Q: find an equation for the plane that is tangent tothe given surface at the given point. z = 4x2 + y2,…

A: It is given that, z = 4x2 + y2, at the point (1, 1, 5) We have to find the equation of tangent…

Q: The unit normal vector to the surface x'y + 2xz? = 8 at the point %3D (1,0, 2) is

A:

Q: Let C be the curve of intersection of the surfaces with equations   x2 + y  =  5   and   24x + 4y…

A: Given: Let C be the curve of intersection of the surfaces with equations x2+y=5  and   24x + 4y + z…

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 an equation for the plane that is tangent to z=4x^2+y^2 at the point (1,1,5)

A:

Q: Find a vector parameterization of the plane −5x−4y−5z=18. r(s,t)=_____? (Use s and t for the…

A: A parametrization for a plane can be written as                                       r = s a + t b…

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

A:

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 a unit normal vector to the surface at the given point. x²y3 - y?z + 2xz3 = 4 (-1,1, –1)

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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)…

A:

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: 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: Find the equation of the plane tangent to and the line (in symmetric form) normal to the ellipsoid…

A: Given:   x2+ 4y2 +8z2 = 48 Point : ( -2 , 3 , -1)

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 2x² + y²…

A: Given: Let us take x = t. So, we get y=t4  and  z=2t2+t42=2t2+t8.

Q: Find a vector parametrization for the line with the given description. Perpendicular to the…

A: Given points are (0,0,8). The equation of yz-plane is given by ⇒x=0 Therefore, the normal vector is…

Q: Check that the point (−1,−1,2) lies on the given surface. Then, viewing the surface as a level…

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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: 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 a nonzero vector normal to the plane z−3(x−4) = −4(1−y) correctly.

A:

Q: Find a vector function that parameterizes the curve of intersection between the surfaces y^2-z^2=x-2…

A: To determine the vector function for the curve of intersection between the surfaces.

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

A: