Hi, the notation used for defining vectors and parameters is just the one in the question and I didn't want to confuse the vector x with a cross product, so I used the other notation for cross product, nevertheless I accept that it was a bit confusing, apologies.
Ok I see this totally, makes...
Homework Statement
Four 3-vectors a, b, c, and d are related by the equation
ax + by + cz = d;
where x, y, and z are real parameters. Using a suitable combination of scalar and vector
products, findd x, y, and z in terms of the vectors
Homework Equations
The Attempt at a...
Yes sorry, wasn't being very clear, I did mean the k component of n hat there yes. Ok I see the problem with the normalisation factor there, should be 4x2 and 4y2, thank you very much!
Homework Statement
(i) Find the normal, n, at a general point on the surface S1 given by; x2+y2+z = 1 and z > 0.
(ii) Use n to relate the size dS of the area element at a point on the surface S1 to its
projection dxdy in the xy-plane.
The Attempt at a Solution
To...
Homework Statement
A wire loop of area 2·0×10−4 m2
contains 40 turns, and has a total resistance of
40Ω. The plane of the loop is perpendicular to a uniform magnetic field of magnitude
B0. The magnetic field is now turned off such that the flux through the loop drops
linearly to zero. A total...
Actually I think I might have worked it out. I think it is just the solutions to z^3=1 so
1, e\frac{2\pi i}{3}, e\frac{4\pi i}{3}
I tried it for the equations and it worked, is this right? They are all rotations of 2pi/3 of each other so it does make sense.
Ok, so does it rotate them by 2π/3 keeping the same magnitude?
But I'm still struggling to work out my problem from this. Do I need to just think about it or can I actually solve the problem using the equations, because I've tried eliminating to no avail?
Ok I think I've worked it out now, I wrote out the differential equation and the auxiliary equation gave me answers of
m=Aex + Bex(\frac{-1}{2}+\frac{\sqrt{3}}{2}) + Cex(\frac{-1}{2}+\frac{-\sqrt{3}}{2})
Which I can solve using initial conditions to get A=B=C=1/3 so the final sum is...
I'm still a little confused I think. I managed to get the the differential equation whose auxiliary equation is m^3-1=0 which is what I solved in the previous section but for complex numbers not real, or does it not matter?
Because if I use my solutions for z^3-1=0 then I end up with very...
Homework Statement
Find the sum of the series
\displaystyle S_1=1 + \frac{x^3}{3!}+\frac{x^6}{6!}+\,\dots
Can't seem to get the bit above to show up nicely, should be 1+x^3/3! +x^6/6! +... Sorry!
Homework Equations
In a prior part of the question I had to find the complex roots of z3-1=0...
I'm sorry I don't know. I thought that the chain rule for partial derivatives was;
\frac{du}{dz} = (\frac{\partial u}{\partial x})y(\frac{dx}{dz}) + (\frac{\partial u}{\partial y})x(\frac{dy}{dz})