Q3) Evaluate both sides of Stokes theorem for the region bounded by: 0
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- b) Write down the two components of the geodesic equation.Use Stokes' theorem to evaluate SF. dr where F = z²î + y²ĵ + xk and C is the triangle with vertices (1, 0, 0), (0, 1, 0), and (0, 0, 1). The unit vector normal is upward. Z -3 2 2 X2) Consider the two vectors à = Agî + Ayĵ and B = Bzî + Byf. If î · î = ĵ • j = 1 and î ·j = j • î = 0, prove algebraically that à · B = A,Bx + A,By.
- Determine F1 and the angle of Theta. If the magnitude of the resultant force acting on the eyebolt is 800N and its direction measured clockwise from the positive x axis theta=30.Determine the angle 0 between the 350-lb force and the line OC.Question 9 Which of the following describe the expansion coefficients for a general state? O an = (En lbn)) |) an = (Vn|b) = S da p (a)p(x) O an = (Vn|Wm) = [ da (x)Vm (x) %3D O an = (n|b)* = S° da n (a)*(x) 8.
- Determine the Miller indices for the directions A, B, C and D shown in the following cubic unit cell.One day, you are driving your car down the highway, and you notice that you are driving well over the speed limit. You apply the brakes of the carapplying a variable stopping force, until the car slows down to a rea sonable speed of 22.4 m/s (50 mph)A computer plots the force versus time for the vehicle and then measures the area under the curve. It is found that the area is - 18.950N . The total breaking time was 5.4 s. Given that the combined mass of you and your car 1sm = 1200 kg how fast were you moving before applying the breaks? What is the average force applied by the road to the car during breaking? (Note: 1Ns=1kg* m/s)Q.) Solve a ,b and c
- 1. Čalculate the gradient Vf of the following functions f(r), where r = Vx2 + y2 + z2: f = In(r). f = r". f = g(r), where g(r) is some unspecified function of r (a) (b) (c)Determine whether the set is a basis for R. If the set is not a basis, determine whether the set is linearly independent and whether the set spans R°. -3 -8 2 Which of the following describe the set? Select all that apply. O A. The set is linearly independent. O B. The set is a basis for R3 O C. The set spans R°. O D. None of the aboveex1