- 1 Choose The Correct Answer For The Questions 1 15 2 Pts Each 1 The Curl Of The Vector Field Fi Siny Cos Z Kis 1 (39.06 KiB) Viewed 26 times
1. Choose the correct answer for the
questions 1-15 (2 pts. each) 1. The curl of the vector field Fi-siny] + cos²z kis (a) ze (b)-revk (e) ze 1-cosy 3-2 cosy sinz k (d) ze-cosy-2 cosy sinz 2. If the gradient of f(x, y, z) at (1,2,3) is 21-23+k, then the maximum value for a directional derivative of f(r.y.
at (1,2,3) is (a) -3 (b) 3 (d) -9 3. If a, b and care nonzero real numbers such that the vector field F-1+yjis a conservative vector field, then c= (a) 7 (b) 6 (c) 5 4. The value of feF.dr where F-1+2r and sint 1-3. Ostsi (c) 1 (a) (b) 0 (d) -1 5. The value of a so that the vectors -1-aj and w-1-3) are orthogonal is (a) 3 (b) (c) (d) = R enclosed between the prabols y and the line 6. Using the double integral, the area of the region y 3r is (a) la 3-a-dyda (b) o dydz (c) ²-3x dyda (d) dyda 7. The sugle between the vectors i = (1,0,3) and = (0,2√√3) (b) (c) (d) 8. Using the chain rule, the value of at u-1, v-1 where 2-6x³y-2+3y, z, y (a)-9 (b) 5 (c) 9 (d)-13 9. The system of ordinary differential equations corresponding to the PDE -2,0<z<1, y>0 is (a) -2A=0 and + Ar=0 (b) r"+A=0 and Ar"-0 (d) r"+2-A=0 and "A (c)"+2r-A-0 and "-1-0 10. Let =(-2,3). The unit vector in the direction of is (b) (1.1) (e) (i) 11. fff dydede (b) (c) 12. The total differential de for the functioneat (1,0) is (a) 2 dy (b) 2 dz+2 dy (c) 2 13. Let and be vectors with =(-1.1.0) then (b) (1,-1,0) (c) (0,0,0) 14. Let (z.), then /(2,1)- (b) (c) (d) 2 dz (d) (-1,1,0)