
iv) Consider a vector field given by: A = E.(cos Of – sin oô). Evaluate: a)...
= Consider the vector field F(x, y) (cos y + y cos x)i + (sin x – xsin y)j. Show whether the function f(x,y) = x COS Y – y sin x is a potential function for the vector field, F.
Consider the vector field. F(x, y, z) = (3ex sin(y), 3ey sin(z), 5e7 sin(x)) (a) Find the curl of the vector field. curl F = (-3d"cos(z))i – (36*cos(x)); – (5e+cos(y) )* * (b) Find the divergence of the vector field. div F = 3e'sin(y) + 3e'sin(z) + 5e+ sin(x)
#3 Consider the vector field F- Mi+ Nj Pk defined by: F- ysinzi+sinjry cos z k. Compute the line integral ScF dr over a unit circle. Compute the line integral ysin z dr+ r sin z dy + ry cos zdz (0,0,0) #3 Use Green's Theorem to evaluate the line integral along the given positively orientated curve C. e2*t d e" dy, C is the triangle with vertices (0,0), (1,0), and (1,1)
#3 Consider the vector field F- Mi+ Nj...
9. Let V(x,y,+) - +w7+ sin(x + y)e'] + cos(x + 2) be a vector field in R'. Compute the curl and divergence of the vector field.
Consider the vector field.
F(x, y, z) =
6ex sin(y), 8ey sin(z), 5ez
sin(x)
Consider the vector field. F(x, y, z) = (6e* sin(y), 8ey sin(z), 5e? sin(x)) (a) Find the curl of the vector field. curl F = (-8e'sin(z), – 5e'sin(x), – 6e'sin(y)) x (b) Find the divergence of the vector field. div F = 6e sin(y) + 8e) sin(z) + 5e+sin(x)
use the info. given below to find sin(a-b)
cos a= 5/13, with a in quadrant IV
cos b= -5/13, with b in quadrant III
O TRIGONOMETRIC IDENTITIES AND EQUATIONS Sum and difference identities: Problem type 3 Use the information given below to find sin(a - b). COS 7 5 with a in quadrant IV 13 5 with B in quadrant III 13 cos B 1 Give the exact answer, not a decimal approximation. sin (a - b) = 0 8...
Find the divergence of the following vector field. F = (4yz sin x, 9xz cos y, xy cos z) The divergence of F is
Consider the vector field. F(x, y, z) = (98 sin(y), 4e' sin(z), 2e sin(x)) (a) Find the curl of the vector field. curl F = (b) Find the divergence of the vector field. div F =
12. Consider the curve given by ř(t) (3 cos(t),4t, 3 sin(t) (a) Which of the images below is the plot of the curve? IV 20 50 (a) Compute the arc length of the curve from t = 0 to t = 3. (b) Find the unit tangent vector T(t). (c) Compute the curvature of the curve at any value of t.
12. Consider the curve given by ř(t) (3 cos(t),4t, 3 sin(t) (a) Which of the images below is the...
Consider the following matrix, As[ cos θ sin θ -L-sin θ cos θ J, for some θ E (-π, π] (a) What is determinant of A? (b) Perform an eigen-decomposition of A (c) What does this matrix do to a vector in R2.