How to show that $(\mathbf{p} \cdot \mathbf{q})^2 + \|\mathbf{p} \times \mathbf{q}\|^2 = \|\mathbf{p}\|^2\|\mathbf{q}\|^2$
38200
Show that $(\mathbf{a}·\mathbf{a})(\mathbf{b}·\mathbf{b})-(\mathbf{a}·\mathbf{b})^2=(\mathbf{a}\times\mathbf{b})·(\mathbf{a}\times\mathbf{b})$?
120642
Let $g : \Bbb N \times \Bbb N \to\Bbb N \times \Bbb N$ defined as $g(m,n) = (m + n,m - n)$
137511
Trying to show that $\sup \{b^p:p\in Q,\;0<p<x\} = \inf\{b^q:q\in Q,\;x<q\}$
5250
Are $T\mathbb{S}^2$ and $\mathbb{S}^2 \times \mathbb{R}^2$ different?
72144
Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
142360
How to show $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$
148355
Regarding Goldstein's claim that $\mathbf{F} = \dot{\mathbf{p}}$
9140
Show $\operatorname{Aut}(C_2 \times C_2)$ is isomorphic to $S_3=D_6$
13902
Show that $\frac{1}{x_1^2}+\frac{1}{4\cdot x_2^2}+\ldots+\frac{1}{n^2\cdot x_n^2}\leq\frac{3n-2}{2n-1}$.
108657
Cross product of the quantum mechanical operators $\textbf{p}$ and $\textbf{A}$
148668
How to show $A\times (B\cup C) = (A\times B)\cup (A\times C)$
88124
$M,N\in \Bbb R ^{n\times n}$, show that $e^{(M+N)} = e^{M}e^N$ given $MN=NM$
14480
Proving $(P(AB))^2+(P(AB^c))^2+(P(A^cB))^2+(P(A^cB^c))^2\ge\frac{1}{4}$ for any events $A$ and $B$
2235
Showing $\text{Aut}_\mathsf{Grp}(\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}) \cong S_3$
29545
$[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$
24585
Proving that $\mathbf{W}$+$\mathbf{W^{\perp}}$=$\mathbb{R^{n}}$
137982
Show that $\textbf{ZF}$ shows $\phi$ is $\Delta_1$