Consider the vector fieldF = zi + aºj+ (y3 + 3z)kCalculate the divergence:V.F =.Calculate the curl, and enter each component in the boxes below:V x F =ikNote: you must enter a coefficient for i, j and k even if it is a number like 0 or 1. It is generally easier to use textinput rather than the maths editor. Use the preview button (magnifying glass) to make sure your expressions arecorrect.Let C be a circle in 3 dimensions parallel to the xz-plane, where2 = 25+and y = 2, traversed anti-clockwise around the positive y-axis.Evaluate the following line integral by any suitable method, rounded to 2 decimal places:F drAdvice: Draw a sketch of the situation. If possible, check your answer using multiple methods, and verify yourcalculations in Maple.

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Consider the vector field F = zi + a2j+ (y3 + 3z)k Calculate the divergence: V.F = Calculate the curl, and enter each component in the boxes below: V x F =, k

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

Consider the vector field
F = zi + aºj+ (y3 + 3z)k
Calculate the divergence:
V.F =.
Calculate the curl, and enter each component in the boxes below:
V x F =
i
k
Note: you must enter a coefficient for i, j and k even if it is a number like 0 or 1. It is generally easier to use text
input rather than the maths editor. Use the preview button (magnifying glass) to make sure your expressions are
correct.
Let C be a circle in 3 dimensions parallel to the xz-plane, where
2 = 25
+
and y = 2, traversed anti-clockwise around the positive y-axis.
Evaluate the following line integral by any suitable method, rounded to 2 decimal places:
F dr
Advice: Draw a sketch of the situation. If possible, check your answer using multiple methods, and verify your
calculations in Maple.

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