Consider one-surface hyperboloid is given by the equation 1. Using the gradient, find the normal vector. Show that they are pointing in the same direction.

Q: find a parametrization of the curve. The line passing through (1, 0, 4) and (4, 1, 2)

A: Given: A line is passing through the points 1, 0, 4 and 4, 1, 2.

Q: 32. Determine the vector equation of the plane that contains the following two lines. L1: = [4,-3,…

A: .

Q: A bee starts at the point (5, 7, -3) (with units in meters) and travels at a constant speed of 9 m/s…

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Q: Determine the direction angles for the line with parametric equations x = 5 + 2t, y = 12 - 8t, and z…

A: Direction angle

Q: A velocity vector of variable magnitude of an object can have a constant direction. O True False

A:

Q: Give a parametric representation for the straight line segment from the point (1,-1,2) to the point…

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Q: 16. Let Li be the line with vector equation r (-2,3) + s(-1,3), s e R. Let L2 be the line with…

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Q: 6. Let A= (1, 2, 0), B = (3, 4, -1), and C= (4, 5, 2). Find the exact value of the distance between…

A: Given- A=(1,2,0) , B=(3,4,-1), C=(4,5,2) To find the exact value of distance between point C and the…

Q: Determine the equation of the plane with a point 'a' and the normal vector 'n': a = (−1, 2, −3)t ,…

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Q: Consider the function f(x, y) = (e* - 2x) sin(y). Suppose S is the surface z = f(x, y). (a) Find a…

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Q: Find vectors u and v such that the parametric equation of the line y= mx + b can be expressed as…

A: Given that  equation of the line is  y= mx + b…