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1. ### Distance between two planes

Ok, keep in mind that the general equation of a plane is Ax+By+Cz+D=0 . It can be proven that the vector \bf{N}=(A,B,C) , called normal vector, is orthogonal to the plane Ax+By+Cz+D=0 . So two parallel planes have a common normal vector \bf{N}. What do you need to be able to talk about the...
2. ### Distance between two planes

Your problem is quite simple but the I way I would solve it requires you to know about vector projection, are you familiar with it?
3. ### On the properties of non-commutative groups

Homework Statement Let [G,+,0] be a non-abelian group with a binary operation + and a zero element 0 . To prove that if both the zero element and the inverse element act on the same side, then they both act the other way around, that is: If \forall a \in G , a + 0 = a , and a + (-a)...
4. ### Probability Question

The union of two probability sets is the probability of A happening OR B happening: The chances of throwing a dice and getting 6 is 1/6, the chance of getting a 2 is 1/6, the chance of getting a 6 or a 2 is 1/6 + 1/6 = 1/3. The intersection of two probability sets, which is the probability of A...
5. ### Probability Question

Um, I might be wrong here, long since my last prob class but I believe you're almost there: For ijk +mn to be even IJK AND MN must be either odd or even, so why not calculate the probability of BOTH being odd (intersection between the chances of ikj being odd and mn being odd), and the...
6. ### Number Theory-limitation of Pn

It is not very elegant but the proof follows from the principles of order on the real number field. Considering positive primes: given p_{1} < p_{2}, then it follows that p_{1} < p_{1}^2 < p_{1} \cdot p_{2}, by inductive reasoning you can prove that p_{n+1}<p_{n+1} \cdot p_{1} < p_{n+1} \cdot...
7. ### Matrix determinant

Huge hint: In the main diagonal of your matrix i = j, so max{ i, j } = i or j above the main diagonal j > i, so max{ i, j } = j below the main diagonal i > j so max { i, j } = i
8. ### Help proving matrix properties:

Homework Statement Let A, B be both matrices with the same dimensions. Is AB^2 = (A^2)(B^2) a valid claim? Homework Equations The Attempt at a Solution I attempted to show that (AB)^2 = (AB)(AB) = A(BA)B and that (A^2)(B^2) = (AA)(BB) = A(AB)B, so for A(BA)B to be equal to A(AB)B, AB...
9. ### Sum and Difference Formulas PROVE

Like Mark44 said, use the fact that A - B = A + (-B). Hint: Sine is an odd function, which means that f(-x) = -f(x) 2nd hint: Cosine is an even function, which means that f(-x) = f(x) That should do the trick.