Consider the vector function r : R - R° given by r(t) = (21² + t, t + 1, 1² – 2), and let C be the corresponding space curve. (a) The plane given by 2x + y – 3z = 5 intersects C at the points (1, 0, -1) and ( (b) At the point (3, 2, -1), the vector 1 is tangent to C.

Q: 2. Let f(x,y) = t Find the direction of a unit vector so that Daf is minimal at point (0, 1). %3D 3…

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Q: A vector normal to the surface y-:=3 at the point (-1-2, 2) is (a) i+2j+k (b) -i+j+2k) (c) (21 -j+k)…

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Q: Let r (t ) = sin t i + et j + In (t + 1) k be a space curve. Which of the following vectors is…

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Q: Match the vector-valued functions (a)–(f) with the space curves (1)–(vi) in Figure 10. (a) r(t) = (t…

A: (a) Identify the graph of the vector function rt=t+15, e0.08tcos t, e0.08t sin t. From the equations…

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Q: Sketch the space curve. Vector-Valued Function r(t) = (5 sin t, 2t, 5 cos t) Interval [0, π]

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A: According to question given thatr(t)=t3 i + t2 j + 1t k

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Q: Sketch the space curve represented by the vector-valued function and give the orientation of the…

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A: Since you have asked multiple questions, we will solve the Question Q(1) and (2) for you. If you…

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A: (a) r(t)=t+15, e0.08tcos t, e0.08tsin t From the function we have x=t+15, y=e0.08tcos t and…

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Q: Match the vector-valued functions (a)-(f) with the space curves- (1)–(vi) in Figure 10. (a) r(1) =…

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Q: Match the vector-valued functions (a)–(f) with the space curves (1)–(vi) in Figure 10. (a) r(1) = (t…

A: (d) map to  (vi) (e)  maps to (iv) (f) map to (iii)

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