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July 23, 2020 12:06 pm 30 pts
STaT. Ttah + 27ta-n EvaluateJJ.F.ds, where F- zi +xj - 3yzk and S is the surface of the cylinder x* + y = 16 included in the first octant between z = 0 and z = 5 A unit vector normal to the surface S(x? + y = 16) is ol. -_2xi 2xi+2yj 4x+4y) xi +yi 4 We have JFids-f F dk dz 2 where R is the projection of S on the x-z plane. It should be noted that in this case we cannot take the projection of S on the x-y plane as the surface S is perpendicular to the x-y plane. Now, Fi-(zi+x-3y'zk) i (xZ+ Xy) 4 herefore, the required surface integral is XZ + Xy dx dz l-4va XZ =+x dx dz = 90 4 y/4 z-0Jx-016-x
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Projection simply means shadow.Suppose a sheet of paper is in xz plane. Can you get shadow of it in xy plane or yz plane.Answer i's no. Here the surface normal n=1/4(xi+yj) is in x...
• Ruby negi
if u took dxdz in numerator ,u have toh take n cap dot y cap or if u take dydz u have to take n cap dot x. hope u r getting.. projection is simply a shadow..
Ruby negi
seee
• Vaishali sharma
protection shows a shadow of something on base. now in question surface is in xy plane so we can't say that it's projection would be in xy plane
Vaishali sharma
hope u would get it
• Ankita
sir ek baat nhii smjh ayii kii es formula mein dx dz kaise smjh ayega and niche n^j^ kaise aya
• Jasman
because surface of integration S is not parallel to any of the axes-xy,yz,zx properly.they are saying surface is included in octant.so,we took projection.and, in xy plane we can't ... 