If F = xy?i + yz? j + zx2k, and S is the region bounded by the triangle with vertices (1,0,0), (0,2,0) and (0,0,3). Use Stoke's Theorem to evaluate, (V × F) · în dS

Q: Compute foxy dx + (x³/2+y³/2) dy where C is the square with vertices (0,0), (0,1), (1,1) and (1,0)…

A:

Q: p) Classify the following models as ARIMA(p,d,q). i) (1-B)x, = (1-0.3B),. ii) (1-0.5B+0.25B²)Vx, =…

A: ARIMA means auto regressive integrated moving average, It ia also written in the forn ARIMA(p,d,q)

Q: Find the cross product u x v where i = 3i +6j +9k and v = (- 2, – 4, 5). ux v =

A:

Q: 2) Use Green's Theorem to compute f F df where F= (3x +4y)i + 2xyj and C is the triangular path from…

A:

Q: Find the condition for the points (a, 0). (h, k){0,b) when ab = 0 to be collinear.

A: Find the condition for the given points to be collinear.

Q: Show that V spans P² where V = {1 + 2t + 2t², t + t², 1 − t²}

A:

Q: (b) Prove that Vx, y ≤R : x² + xy + y² ≥ 0, and that x² + xy + y² = 0 if and only if x = y = 0.…

A:

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

A:

Q: For which values of ß does {(1,0, ß),(1,2,–3)(B,1,0)} span R'?

A: If spans the same subset of R³, the vectors must be linearly dependent to each other.    Therefore,…

Q: Give an example of (v1, v2, v3) and (w1, w2, w3) independent se- quences in the R“ such that…

A:

Q: Let C1 be the line segment from (1,0,1) to (0,3,6). Evaluate dx + dy + dz.

A:

Q: || x dA, R is bounded by y = x, 2x + y = 6 and the y-axis. R

A:

Q: A rectangle ha verices at P (6, 6), Q (6, -6), R (-6, -6) and S (-6, 6). The origin is the center of…

A:

Q: [1 |A = [a1, a2, a3, a4] 2 11 5 0 3 -1 4 0

A:

Q: Use the Jacobian of a coordinate transformation to find the area of the parallelogram bounded by the…

A: We use the following transformation to find the area of the parallelogram bounded by the lines y =…

Q: Use Green's Theorem to evaluate $. xydx + x²y³dy, where C is the triangle with vertices (0,0), (1,0)…

A: Consider the provided question, ∮cxydx+x2y3dy,     where c is the triangle with vertices 0,0, 1,0…

Q: c. Let P(x, y) = y² + sin¬1 x² and Q(x, y) = 2xy + 4x. Suppose that C is the parallelogram with…

A:

Q: Given Fxy 2) = (z², xy, yz) and C is a triangle in the plane x + y + z = 2 with vertices (1,1,0),…

A: We will use basic knowledge of vector calculus.

Q: Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the area of the triangle UVW

A: