Multivariable Calculus 9 questions assignmentHello,please see attachment for the assignment and try to solve it ( clear handwriting ) please try to use this book for answering the questions. the book name: Calculus: Early Transcendentals (3rd ed), by Jon Rogawski

Multivariable Calculus M273 Name:Section:Show all work and use correct notation for full credit.1. (1 Credit) Answer “True” or “False” for each of the following statements by darkly shading the appropriatebubble. No justification required.(a) True False If the reading on a car’s speedometer is constant, then the car cannot be accelerating.(b) True False The curvature of a line is zero.(c) True False The two lines parameterized by r1(t) = ht + 1; 3; 2 – ti and r2(t) = h2t + 2; 2t + 3; t + 1iintersect at the point (2; 3; 1).(d) True False If u; v, and w are vectors such that u · v = 0, and v · w = 0, then u · w = 0.2. (2 Credits) Find an equation for the line tangent to the curve r(t) = pt2 + 4; sin (2t); et at the point (2; 0; 1).Page 2 of 73. (1 Credit) Find the equation of the sphere centered at the point (-3; 2; 4) that lies tangent to the yz-plane.4. Consider the three points P (2; -3; 4); Q(0; 1; 2) and R(-1; 2; 0):(a) (1 Credit) Find –! PQ and -! PR:–!PQ = -! PR =(b) (1 Credit) Find a vector orthogonal to both –! PQ and -! PR:(c) (1 Credit) Find the area of the parallelogram spanned by the vectors –! PQ and -! PR.(d) (1 Credit) Is the parallelogram from part (c) a rectangle? Justify your answer using calculus, anddarkly shade the bubble corresponding to your choice.Yes No(e) (1 Credit) Find an equation for the plane through P; Q and R. Express your answer in the form ax+by+cz =d for constants a; b; c; d.Name and section:Page 3 of 75. Provide clear sketches of the designated traces for the surface 4×2 – y2 + 4z2 = 4. Make sure to label youraxes.(a) (1 Credit) y = 0(b) (1 Credit) y = 2(c) (1 Credit) z = 1Name and section:Page 4 of 76. (1 Credit) For each of the following equations, indicate the letter of the picture that most resembles the graphof the given surface by darkly shading the appropriate bubble.(a) x2 + z2 = y2A B C D E F(b) 4×2 + 4y2 + z2 = 4A B C D E F(c) x2 + (y – 1)2 + z2 = 1A B C D E F(d) x2 + 2z2 = 8A B C D E FA.-22-22-2-12 1B.-22-22-22C.-12 12-12 1D.-4-24 2-4-224-22E.-2-12 1-22-12 1F.Name and section:Page 5 of 77. (2 Credits) Given u = 3j + 3k and v = -i + j + k; find vectors a and b with the following three properties:1. u = a + b2. a is parallel with v:3. b is perpendicular to v:a = b =Name and section:Page 6 of 78. For a positive constant a, consider the curve r(t) = a cos (t); a sin (t); p3at : Compute the following:(a) (1 Credit) The arc length of the curve from t = 0 to t = 2π.(b) (1 Credit) The unit tangent vector T(t) at time t = π:T(π) =(c) (1 Credit) The unit normal vector N(t) at time t = π:N(π) =(d) (1 Credit) The curvature of the graph of r(t) at t = π:κ(π) =Name and section:Page 7 of 79. Suppose a fly moves around a room with position given by the vector-valued function r(t) = i + tj + t2k, for0 < t < 1.(a) (1 Credit) Find the speed of the fly as a function of t.(b) (1 Credit) In order to catch the fly, a person places flypaper along the plane with equation -x + y + z = 1.Will the person succeed in catching the fly? If so, at what point in space will the fly hit the flypaper?

Problem
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Credit
1
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1
5
3
1
2
4
2
21

Credits Earned
Name and section:

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