a) If A=xz' i-2x²yz j+2yz k, find VxA (curl A) at the point (1,-1,1).

Q: Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].

A:

Q: e'ス+×cos(2) 3. (o'1'e)と Flsye)-xをえゃxそsQe)s Find Curl at

A:

Q: 18)Find curl F and div F if F(x,y,z) = exsiny i + esinz j + e²sinx k

A:

Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: Sketch the curve r(t)=f°i+tj and indicate the orientation. Find r'(t) and sketch r(1) & r°(1).

A: First we will plot the given parameters.

Q: (a) (b) Let V = F" and let A EMnxn (F), F is complex field. Prove that (x, y) = (4¹x, y) for all x,…

A:

Q: Suppose F 2.xz + 3y²) ay + (4yz²) az. (a) Calculate fLL F dS, where S is the shaded surface in…

A:

Q: 1. Use isoclines to sketch the direction field for y' = x+ 2y and sketch the solution curve that…

A:

Q: Show that Sa fdx + gdy = Sa - (16x*y²dx + 8yxʻdy) is independent of path: (10,5) –2) (10,5) ,-2) 4…

A: We are given a line integral as follows : ∫1, -210, 5 fdx+gdy=∫1, -210, 5 -(16x3y2dx+8yx4dy)   First…

Q: Let Compute дw -(-2,-2) = -(-2,-2) = მs дw St W = 2xy - 2yz + 3xz, x = st, y = est, z = t² =

A: