Find equations of the following. 2(x − 5)2 + (y − 1)2 + (z − 9)2 = 10,    (6, 3, 11)   (a) the tangent plane   b) (b) the normal line (x(t), y(t), z(t)) = ?

Q: a) Find an equation of the tangent plane to the surface at the given point. xyz = 15, (1, 3, 5) b)…

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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 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 the equation for the tangent plane and the normal line at the point P,(1,2,2) on the surface 2x…

A: Solve by using formulas of tangent plane and normal line

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

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Q: The equation of line normal to f(x) = (x +4)^(1/2) at Q (0,3) is

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Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: Find the symmetric equations for the normal line LN to the surface S:f (x, y) = 5Vx2 + y? at the…

A: if  f is  function of (x,y,z) then gradient of f is defined asfx i + fy j + fz k ∇f is the normal to…

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

A: Given that x=2 sin3t , y=2t and z=-2cos3t and point 0,π,-2 find equations of the normal and…

Q: (a) Find the directional derivative of φ = x2 + sin y −xz in the direction i+ 2j−2k at the point (1,…

A: a) Given that φ=x2+siny-xz Now first evaluate gradient of φ, so…

Q: Find the equations of (1) tangent plane and (2) the normal line to the given surface at the…

A: Equation of tangent plane at x0, y0, z0 is, z-z0=∂z∂xx-x0+∂z∂yy-y0 Equation of a line with normal…

Q: 6. Find an equation of the tangent plane to the surface z = y² – x² at the point (-4, 5, 9).

A: Recall: Equation of the tangent plane to the surface z=f(x,y)  at (x0,y0,z0) is        fxx-x0 +…

Q: Q3A) Find normal line and parallel plane to the function f(x, y, z) = x²y²z² - 4 At point (1,-1,2).

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Q: Find the gradient of a normal line to the parabola y=x^2+5x-9 at the point (1,1)

A: In this question, the concept of slope is applied. Slope A line's slope or gradient is a number that…

Q: 6. Find an equation of the tangent plane and a set of symmetric equations of the normal line to the…

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Q: Find parametric equations of the normal line to the surface z = + y? at the point (2, -2,5) x = 2 -…

A: Let F(x,y,z) define a surface that is differentiable at (x0,y0,z0) then the normal line to F(x,y,z)…

Q: 2. Find equations of the normal plane and tangent line to the curve of intersection of the surfaces…

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Q: 1. Find the equations of the normal and osculating planes of the curve x = Int, y = 2t, z = t? at…

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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 an equation for the tangent plane to z-x-y = 3 at the point (2, 1, 8) Z - ) %3D

A: given z-x2-y2=3 at point 2,1,8

Q: The equation of the normal line to the curve y = -Vx that is parallel to -6x +y = 1 (A) y + 3 = –6(x…

A: equation of curve y=-x equation of line -6x+y=1

Q: Find the equation for the tangent plane and the normal line at the point Po(3,3,1) on the surface x…

A: To find an equation for the tangent plane and the normal line at the point (3,3,1).

Q: 8. Find the equations of the tangent plane and the normal line to y +z – x=2 at (-1, 1, 0).

A: Consider the given equation: y2+z2-x=2fx,y,z=y2+z2-x-2 Calculate the partial derivative with respect…

Q: Find the equation of the normal line to the paraboloid z = 2x² +y² at the point (1,2,6). Select one:…

A: Equation of paraboloid  To find: The equation of normal at a point P = (1,2,6).

Q: b) Find equations for the tangent plane and normal line at the point P-(2, –3,18) on the surface…

A: x2+y-2xy-x+3y-z=-7   Let fx,y,z=x2+y-2xy-x+3y-z+7 and the point is 2,-3,18 Now,…

Q: The equation of the normal line to the curve y = -Va that is parallel to -6x+y = 1 (A) y + 3 =…

A: given,     curve y=-x is parallel to -6x+y=1

Q: Find the equation for the tangent plane and the normal line at the point Po(3,2,3) on the surface 2x…

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Q: 6. Find an equation of the tangent plane and a set of symmetric equations of the normal line to the…

A: Let's find.

Q: Find an equation of the normal line to the surface z = ye 2æy at the point (0, 2, 2).

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Q: Find the equation of the tangent plane and normal line to the function f(x,y)= \x +y at the point…

A: Please see the explanation below

Q: 4. Find an equation of the tangent plane to the surface z=- xy+8 at the point (1,1,-10) ху — 2х

A: Equation of tangent plane is: {df(x0,y0)/dx} (x-x0)+{df(x0,y0)/dy} (y-y0)-(z-z0)=0

Q: 4. Find the equation of the tangent plane to the surface ew + In(xz) - evz = 0 at the point (1,0,…

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Q: If the equation of the tangent plane to x2+y²-83z2=0 at (1,1,/2/83) is x+ay+Bz+y=0, then a+ß+y=

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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: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 12, (1, 3, 4) (b)…

A: Given: xyz=12 (1,3,4)

Q: vember 12, 20Z1 m # 3 Find an equation of the tangent plane to the face at the given point. f (x,y)…

A: Solve the given problem.

Q: 3. Find the equation of the tangent plane and the equations of the normal line to the surface z = In…

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Q: Find the equation of the tangent plane and normal line to the surface at the given point. x2 z = 9…

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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 parametric equations for the normal line to the surface -10x + 5y + 9z =3 at the point (1, -…

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Q: Find an equation of the tangent plane to the surface at the given point. x² + y2 + z2 = 33, (1, 4,…

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Q: 3. Find the equation of the plane tangent to xyz + x² – 2y² +z' =14 at (5,–2,3)

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Q: Find equations for the tangent plane and the normal line at point Po (Xo Yo.Zo) (5,2 on the surface…

A: We know that the equation of the tangent plane is: nxx-x0+nyy-y0+nzz-z0=0 Given:…

Q: (a) Find an equation of the tangent plane to the surface at the given point. z = x² - y², (5, 3, 16)…

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Q: Find the equations of the tanget plane and normal line to the graph of In(z2) x -= 3y³ – Vx at the…

A: Given graph is                                                        lnz2x-eyx=3y3-x Again…

Q: Find all equations of normal line at the point (1, 1, –1) to the surface 2 +z² +3 = 2y + y?…

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Q: Find parametric equations of the normal line to x2 the surface z = 4 + y? at the point (2, 3, 10)

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Q: 7.) Find an equation of the tangent plane to the surface, x y(2z-3), at the point P(4,4,2)

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Q: 10. Find a tangent plane to z² – x² +y² = 1 at (7, –5, 5).

A: To find a tangent plane to the given curve at the point (7,-5,5)

Q: 1. Find the equations of the normal and osculating planes of the curve x Int, y 2t, z = t2 at the…

A: Equation of the plane :  r→.n^ =a→.n^ ; where 'r→' is the position vector and 'a→' is the given…