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- Solve the Gradient, divergence and curl of the following vectors F = x²yi (2³-3x)j + 4y²k 1. ‚ F = (3x + 22²) i + ªª³y³² j − (z − 7x) k - - 2 2. F = (2y — cos(x)) i — z²e³xj + (x² − 72) k - - 3. 4. 5 F - (4y - 1) i + xy²j+ (x − 3y) k - == 4y F = 2² (y − x) i +¹¹ j + (x² − 3x) k 3Q1) Find the canonical form of these question : a) fx.y.2) = F=x' y z+x y' z +x yz b) f(x.y.z) =F=x' y z+x y'z" +x y z4) Find the orthogonal trajectories of the family of curves x? + Y? = R?
- Determine the orthogonal trajectories of the family of electric field lines described by the family (x-c)3 + y2 - c2 (3x-c) = x34. Find x and y such that z=xy subject to *+y= 36, x20, y20 attains a maximum value. A) (24,12) (23,13) C) (25,11) D) (22,14) E) (18,18) B) Ans: A4) Determine whether the given set of functions is linearly independent on the interval (-x,). a) (z) = cos 2z, (2) = 1, 1,()= cos z b) (z)=z, 1,(2)=z-1, (z)=z+3 c) ()=e**, 1,(=)=e
- The orthogonal trajectories of Y = ce",where cis arbitrary constant. is – 2x + 2C = 5y² 2x + 2C = 5y² x + 2C = 5y² O -2x + 2C = y?Find the linear approximation of fcu) In n around n= e Using this equation, y= f(a) +f'ca)(X-a)Find the 2. equation of the place that Pusses +2 through the point= (-1,2,1) 3 Contains the line of intersection of the places Vty -7-2 3 zxay +3z=| (12)23,20271115) Xy2z-9 -121212/0 02/02 Paile 2,350