Consider the line perpendicular to the surface z = x2 + y at the point where x = 1 and y = -1. Find a vector parametric equation for this line in terms of the parameter t. Enter your answer using vector notation < x(t), y(t), z(t) >. L(t) =

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A: To Sketch the plane curve represented by the vector valued function Give the orientation of the…

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A: Let C be the curve of intersection of the hyperboloid x2 - y2 + z2 = 4 and the plane , 2y - z = 0.…

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A: Given,              rt=2t2+3i+15t-7j+4t2+5kand  passing through the point P-3, -22, -7.

Q: Represent the plane curve by a vector-valued function. x- + y2 = 4 r(t) = 2 cos ti +2 sin tj

A: x2 + y2 = 4 x2 + y2 = 22 = r2 Therefore, r = 2

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A: Given that: 5y-3x+z=9 Let x=u cos v, y=u sin v So z=9+3x-5y  =9+3u cos v-5u sin v

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A: Given the curve     rt=2sin(t),2cos(t),4sin2(t) and the point P1,3,1.

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A: Given that rt=3cost,3sint,9 P32,32.9 To find the parametric equation for the line tangent to the…

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A: Detailed explanation mentioned below

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A: Given: The planes are -8x-2y-5z=0 and -4x+2y-9z=0 To find the parametric equation xt, yt, zt

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A: here we will find angle between two planes and parametric equation of plane's line of intersection,

Q: Give the length of a curve given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in…

A: given parametrically by x = x(t), y = y(t), and z = z(t) for a ≤ t ≤ b in the vector form.

Q: Find the length of the parametric curve x = e^t + e^-t, y = 5-2t on the interval [0,3]

A: Find the length of the parametric curve x = e^t + e^-t, y = 5-2t on the interval [0,3].

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Q: Find an equation of the tangent plane to the parametric surface. x = u + v, y=6u^2, z = u − v. at…

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Q: express the parametric curve in the form y = f (x) c(t) = (4t − 3, 10 − t)

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Q: Find the unit tangent vector T(t). r(t) = ti + tj+ k, P(4, 2, 8/3) T(2) = Find a set of parametric…

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Q: Find the parametric equation for the line where the planes 7x – 6y + z = 10 and 2x + y – 3z = 4…

A: We have, r(t) = (0, -2, -2) + t(17, 23, 19) The detailed solution is as follows below:

Q: Find the length of the parametric curve x = 2t + 1, y = 3 + 2tž, 0 < t <%.

A: Find the Length of the curve

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Q: Find a vector parametric equation for the ellipse that lies on the plane z (x + 2 - cylinder x + y =…

A: Dear student. You have posted many parts, according to the policy we will answering the first part.…

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Q: Convert the line determined by the symmetric equations x – 5 y +1 z 3 to parametric form. a(t) y(t)…

A: Given symmetric equation of the line is x-55=y+13=z-9 which we need to convert into parametric form

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