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a) Find all values of b for which the vectors <2,1,0> and <0,b,1-b> are orthogonal
2*0+1*b+(1-b(0)), b=0
b) Compute the cross product of
c) When v is a nonzero vector, describe geometrically what vectors w satify
...
w=|v||w| when v is nozero, w may be nonzero, cos=-1, theta=pi
a) Express <4,-2> as a linear combo av+bw, v=<1,1> w=<0,1>
1a+0b, 1a+1b, a=4, b=-6, 4v-6w
b) Give an example showing u
...
w where v is not w
<0,1,0>
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<5,2,3>
a) cylindrical to rectangular (5,pi,4)
(5cosπ,5sinπ,4)
b)rectangle to spherical (4,0,4)
(4√2,0,π/4)
c)find radius and center of sphere ρ=10cosΦ by going to Cartesian coordinates
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<3cos3pi+1,-3sin3pi>=2(3cos3pi+1)-2*2(-3sin3pi)=0
a)find fxyx for f(x,y,z)=y^3 e^(3yz) + xy^2/z^3 + 6x^2 y
dx, dy, dx = 12
b) Calculate the direc
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in the direction <1,2,2> at point (1,0,-1)
f(x,y,z)=xz^2 e^y
fx,fy,fz at point is <1,1,-2> unit vector=1/√9 = 1/3, 1/3*<1,1,-2>*<1,2,2>=<1/3,2/3,4/3)=-1/3
Find the cp of the function
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p
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D>0=(fxx>0 local min, <0 local max) D=0=ind
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max of f(x,y)=xy-5 on x^2+4y^2<=200
0=fx=y, 0=fy=x, (0,0) c
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01)^2 √24
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01)+4/10(-
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calculate the dot
product F(c)*c’ dt for the parameterization of C F(c)=<3t^-2,3t^2), c’=<1,-t^-2>
taking the dot prod
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Fds for F=<4,y> quarter circle x^2+y^2=1 x<=y<=0, counterclockwise
F(c)*c’=−4 sin t + 1/2sin2t then integrate from pi to 3pi/2
Let F= ...
Find the vector F=Gx, F=<3,12y>, evaluate the line integral of F over
c(t)=(t,2t^-1) for 1Find a potential function of F or determine that F isn’t conservative

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Title: Calculus 3
Description: this is a sheet comprised of the main attributes I was taught in calculus 3

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