Question

2. (True / False) The vector field is irrotational but not incompressible. F(, 9, 2) = 2 +y+22) * + y2 +%2' 2 + y2 +2 ,

Answer 1

We are given F(x, 4,2) (Engliz 4 z x² + y² + 2² x² + y² + 22 x²+4² + 2? An innotational vertor field is a rector field where of vector is cuil zuro. Ñ X 11 . كه ola a 2x olot a dy resolan z Y z mayiza x + y + za x² + y² 22 z پاد) x² + y² +2² po tytus-)) dy x² + y² + z + z x²+4² +2² 2 ax x²ry ²+za Ә 2 (od letyn 3 (a ay yoz)

[ 234 (x®+ya +2°)? + - 2x3 (x+y+3)2 -( - 223 | (x2+ y +32) sve)] + Qxy [ - ( - Qxy (x*+ya +32) २ (1P+y2+32) ilo) + f(0) + 0) - T XF 0 irrotational field =) The vector field is an An incompoussible vector is also known as solenoidal vector where the divergence of vector field is zouo. JF [ 64ve) + Get fire) + Gyuz-):). î2 + 1 2 + ² [ ax ay 22

a + 2 4С (ity-uza) dý (1**y*24) * 2 Gamintza + - x² + y² + 2² (x +y + 2)2 -y² + x² + 2² (x+y*+2%) + -2°+1° +y? (x²+4²+2²) x² + y² + 2² (x++y? +2)? 1 x² + y² + 2² J F = 0 =) The vector field is not an incompressible field - The given statement is true.