F. dr For any two paths Cị and C2 in some domain D with same initial and end points, the line integral is independent of

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F. dr For any two paths Cị and C2 in some domain D with same initial and end points, the line integral is independent of path,then (A) Sc, F. dr Sc, F (B) Sc, F.dñ = Sc, F.di (C) Sc, F.di < SoF di (D) SC, F.di > Sc, F.di Select one OA <<< O B. < O C. ces O D. <<

ESTION 11 yet answered If a vector field F-is conservative and curve C is closed then ScF.di is Ked out of 2 Flag stion (A) (A) - (B) (B) °(B) - (A) (C) (D) (A) + °(B) Select one: OA <<< OB <<< O C. <<< OD <<<

One way to find the point on the plane 2x + 3y +z = 1 that is closest to the origin first select a point (x, y, z) on the plane and then minimizes a certain function f(x, y) of two variables Which choice for f is suitable? V (a) (b) (c) (d) (e) Vx2 + y2 x2 + y2 + (1 – 2x – 3y)2 x2 + y2 – (1 – (2x)2 – (3y)) Зу (2x)2 – (3y)2 2.x Select one O a. <<< Ob. << O C. << d. <<< O e. <<<

The number of vectors of unit length perpendicular to the plane of vectors ã = 2i +j+2k and 7 = j+ k is: Select one: O A1 O B.2 O C.3 O D. Infinite

If the vector field F = (x + 2y+mz) î + (2x – 3y – 2)Î +(4x – y +22)Â is irrotational then the value of m is (A)-3 (B) 3 (C) 4 (D) -4 Select one O A <<< OB. <<< O C. << OD <<<