1. Sketch, by hand, the following vector fields by sketching a few representative arrows: (a) F = (0, 1) (b) F = (0, x) (2) P-(√²+P' F= (d) F = (y, - x) Y √x² + y²¹ √√√x² + y² 2 /

Q: 4 В T(t+h) A 21 y 01 2

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Q: 1. Consider the pointsS= (1,−3) andT= (2,5).(a) Sketch the vector−→ST.(b) Give the component form…

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Q: 2y X in the direction of (1, 2). Then, Suppose f(x, y) (a) ▼ f(x, y) = (b) ▼ ƒ(6, π) = = = sin (c)…

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: (b) (c) Given that a(x)=0, show that ã•(¯ × (c − ã))=ã ● (ã×b). Hence, given that à =, b = and c =,…

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

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Q: For this problem, enter your vectors with angle-bracket notation: , not in ijk- notation. (a) F =…

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Q: Suppose temperature °F in a region of 3-space, measured in meters, is given by T= 100 1+ (x − 3)² +…

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Q: (a) y7 + x] (b)-y7 +x7 (c) x7 + y7 (d)-y7 + (x+)7 (e)-y7 + (x-7 (f) (x - y) 7+ (x - y) 7

A: We have to match the vector field

Q: Find a vector in the plane parallel to the line ax + by = c.

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Q: 10. A drop of water falls on the surface z³x+z¹y² + x²y³ = 79 at the point (3, 2, 1). Find a three-…

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Q: At time t=0, a particle is located at the point (3,9,4). It travels in a straight line to the point…

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Q: Suppose that over a certain region of space the electrical potential V is given by the following…

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Q: Let T: R2 R be a reflection in the line y = x. Find the image of each vector. (a) (0, 8) (b) (1,-1)…

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Q: In R, evaluate the alternating 2-form 5 = -3 · dx A dy on the pair of vectors (a, b) if a = (4, 2,…

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Q: Find the vector equation of the line that contains the points (-17, 10,2). r(t)= ( ) +t ( and

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Q: 2.30 Let r denote a position vector r = x= xê, (r² vector. Use index notation to show that: (a) ²…

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Given data net velocity (v) V=x-y, z+y+9, z2 net equation  y=1-x2-z2   , y≥0 find  ∫∫sv.ds= ? in…

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Q: Suppose that the vector-valued function F(t) = < 3t, cos(5t), sin(5t) represents the position of an…

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Q: ) Find the directional derivative of the function f(x, y) = sin²(xy) at the point P (2,7) -2i+j √5…

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Q: Suppose the straight lines L₁ and L2 have respective vector equations 5 4 r1 = -3 + t 3 where s and…

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Q: Explain how to find a vector in the direction of the line segment from P0(x0, y0, z0) to P1(x1, y1,…

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Q: Suppose f(x, y) = √tan(x) + y and u is the unit vector in the direction of (1, 1). Then, (a) ▼ ƒ (x,…

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Q: 19) Consider the vector function 7 (t) = (cos (3t), sin (3t) , 3t). Write 7" () in the form at () T…

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Q: Match the following vector field to its corresponding plot. (a) F₁(x, y) = (x, y) (b) F₂(x, y) =…

A: The vector fields are : The main aim is to match the vector fields with the corresponding plot of…