How prove this $|a-b||c|\le|a-c||b|+|b-c||a|$ if $a,b,c$ are vectors?
88956
For any three vectors $x,y,z\in\mathbb{R}^d$, we have $ \|y-z\|\cdot\|x\|\leq\|x-y\|\cdot\|z\|+\|z-x\|\cdot\|y\|$
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
83449
Proof with 3D vectors
57125
Prove the distributive law $a(b+c)=ab+ac$ for real numbers?
54170
Prove that $\triangle ABC$ is equilateral, If $(a+b-c)^{a}\cdot (b+c-a)^{b}\cdot (c+a-b)^{c}\geq a^a\cdot b^b\cdot c^c$
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
23080
Prove that $a^2(b+c-a)+b^2(a+c-b)+c^2(a+b-c) \leq 3abc.$
65280
If $a, b, c >0$ prove that $ [(1+a)(1+b)(1+c)]^7 > 7^7a^4b^4c^4 $.
127380
Use vectors to prove $\cos(\beta - \alpha) = \cos \alpha \cos\beta + \sin\alpha \sin\beta$
5149
Show $\binom{a}{b}\binom{b}{c}=\binom{a}{a-c}\binom{a-c}{a-b}$
111665
How prove this $\{a\}\cdot\{b\}\cdot\{c\}=0$ if $\lfloor na\rfloor+\lfloor nb\rfloor=\lfloor nc\rfloor$
23869
Prove the implication "if $ac>bc$ and $c>0$, then $a>b$" using the contrapositive
51321
Prove that $A = B = C = D$
64108
how to prove $a+b-ab \le 1$ if $a,b \in [0,1]$?
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
81794
Prove that $(ab,cd)=(a,c)(b,d)\left(\frac{a}{(a,c)},\frac{d}{(b,d)}\right)\left(\frac{c}{(a,c)},\frac{b}{(b,d)}\right)$