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Explain in detail, using definitions and diagrams as needed, what exactly a scalar integral represents
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- Find the line integral of F(x, y, z) = x°i + y°j+ zk along the line segment C from the origin to the point (4, 2, 6). F. dr =QUESTION 1 Give a physical interpretation of what is meant by the curl of a vector. Suppose a vector function A is given by A=-yi + xj and another vector function B is given by B = xj. 1.1 1.2 1.3 Calculate (i) the curl of A: (ii) the curl of B: V x A and Vx B. In which direction are the curls pointing? Hence what can you say about their divergence and why?For part 3, you did the integral with respect to y since it was on the y axis, but you came up with the integral of (y+y)dy. How did you get zero from that statement?
- 1.4 Please answer these (a,b,). Explain well your calculations and steps! Thank you!!! A) Uses the scalar vector product to check if the three points J(-3, -4), K(5, 0) and L (2,6) are the vertices of a right angle. B) The speed of an aircraft is 415 km/h according to a 120° cap. A wind of 30 km/h blows at 45°. C) Determines the velocity vector resulting from the aircraft in relation to the North. (Do this problem by algebraic representation.) 3. Determines a unit vector going in the opposite direction to the vector at = 1-2,4].Plot the graphs of f(x) = x^2 and y(x) = √(4-x^2), where x [-2; 2]. Calculate analytically the overlap integral between these functions on x [-2; 2] (show all steps). Show the overlap on the graph and explain why the value is what you have calculatedPlease calculate and simply this integral
- Read the problem carefully and provide complete solutions with derivation of formulas(integrals and derivatives). Write complete units and solution neatly. Final answer are given after the problem.Show a[1 2 1] direction on a simple cubic unit cell and give the location (in correct notation) for each position where the direction vector pierces the unit cell.hi please solve this question , please make sure its correct , write integral equation only
- Given the points in space, A = (4,2,– 3), B = (-2,5,1), and C = (5,1,– 2) A) Find a parametric set of equations for the line through point A parallel to the line through points B and C. B) Find the equation of the plane containing points A, B, and C using a vector approach (from chapter 11). C) Find the coordinates of a point on the plane other than A, B, or C which does not lie on a coordinate axis. (no 0 coordinates)P. Fig.1 Fig.2 Say you have an infinite sheet lying on the yz plane. A point pi is located at (-10, 11, 11). This is shown in figure (Fig. 1). and (Fig. 2). Note that both figure represent the same thing in 3D (Fig. 1) or in 2D (Fig. 2). And in 2D diagram the Y axis represents the infinite sheet. Note : All coordinates in this problem are in centi meters. a) Find the magnitude of the electric field due to the sheet at pi if the charge density of the sheet is 01 = -15 µC/m² . NConsider a rectangular surface of length L and width W in the xy plane with its center at the origin: Which of the following are valid expressions for the area vector of this surface? Check all that apply. O (0,0, LW) O (W, L, 0) O (0,0, -LW) O (LW, LW, 0) O (0, LW, 0) O (L, W, 0)