The normal vector to the tangent plane for the surface x²y³ z = 8, at the point (-1, 2, 1) is: 2 3 Select one: O-16, 12,8 > O 16, 12, 12 > O-16, -12, -8 > O-16, -12,4 > O None of them

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A: Let P be the point 1,1,3.Q be the point 0,1,2 on the line.Then, PQ→ = 0-1,1-1,2-3=-1,0,-1And the…

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…

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Q: The vertices of AJKL are J(-3, 4), K(3, 0), and L(-5, -4). The equation of the median JLis y = 0.…

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Q: The normal line to the surface x² + 2y² + ² = 25 at the point (1, -2, 4) is parallel to the vector O…

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Q: 2. Find a vector that is perpendicular to the surface x² + y² + z² = xyz + 8 at the point (1,2,3).

A: Given that x²+y²+z²=xyz+8 At (1,2,3)

Q: Find a vector parametrization of the line through P = (3, -5, 7) in the direction v = (3, 0, 1)

A: Given:P=3,-5,7v=3,0,1

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Q: Li Syaoran is riding an airplane which departs from an airport located at (360, 0) miles in the…

A: The westward speed of the airplane = 480 miles/ hour The northward speed of the airplane = 120…

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 the solution set of x1 + x2+2x4 What are the equations of the plane at (1,2,3,4) which is…

A: First we find direction vectors of the plane of solutions.

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Q: 7. On a two-dimensional plane, sketch the vector |v>= such that it emanates from the coordinate…

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Q: Which of the following is a unit normal vector to the plane with Cartesian equation 2x-y+22-5 - 0?…

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Q: Find the value of d in the equation of the plane ax+by+cz+d=0 passing through the point P(3, 1, -2)…

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