The normal vector to the tangent plane for the surface xy² z³ 2 3 = -4, at the point (1, 2, -1) is: Select one: O None of them O-4,-4, 12 > O-4, -4,3 > O4,-4, 12 > O <-4,-4, -12 >

Q: Calculate the distance from point A(1, 2, 1) to the plane of equation 3x-4y + 5z = 1.

A: To find distance of point to plane using the formulae: Given point is and plane equation is .

Q: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2,…

A: Given points A0,0,0 , B2,0,-1 &amp; C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

Q: Let L be the line through the point Q = (- 6, - 9, - 10) and direction vector d = [- 1, - 2, - 2]^T.…

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Q: he vector v = , is tangent to the surface x2 + 2y3 - 3z2 = 3 at the point (2, 1, 1).  Find a.

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Q: Find a vector tangent to the curve of intersection of the two cyclinders x2+y2=32x2+y2=32 and…

A: Solution: The objective is to find a vector tangent to the curve of intersection of the two…

Q: The vector n = (2, -3, 6) is normal to the tangent plane to z = h(x, y)at (1, -3, 5). Estimate…

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Q: Suppose ƒ(1, 2) = 4, ƒx(1, 2) = 5, and ƒy(1, 2) = -3. Find an equation of the plane tangent to the…

A: Equation of the plane tangent to the surface  z=f(x, y) at (a, b) is z=fa, b+fxa, b(x-a)+fya, b(y-b)

Q: x-2 z+4 • Let L:*²=+3 = 2²+ and M: 2x - 3y +z = 6 are line and 3 2 5 plane and let P be the…

A: We have to find the equation of line

Q: Find the equation of the tangent plane to x2 the surface z = 4 + y? at the point (2, –2, 5)

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Q: Find the tangent plane to the equation z = 5x² + 3y² − 3y at the point (5, 4, 161) z =

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Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: Find a plane containing the point (2,2,-5) and the line r(t) =&lt;-6, -3, -7 &gt; + &lt; 6, -6,1…

A: Steps are explained in the image:

Q: Let L. be the line passing through the point P-(4, -3, 1) with direction vector a-[-4, 1, 1], and…

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Q: The normal vector to the tangent plane for the surface x²y³ z = 8, at the point (-1, 2, 1) is: 2 3…

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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 an equation of the tangent plane to the surface at the given point. X²+y²+z²=14, (1,2,3) And…

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Q: By vector methods show that the line x = y = (1/3)(z + 2) is parallel to the plane 2x - 8y +2z = 5..

A: Any arbitrary point P0 on the line can be determined to be as:

Q: Suppose that z is an implicit function of x and y in a neighborhood of the point P = (0, −3, 1) of…

A: Equation of a line passing through point (a, b, c) and parallel to vector &lt;p, q, r&gt; can be…

Q: Find vector and parametric equations of the plane that contains the two intersecting lines † =…

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