ans

000293
(1) $(\dfrac 73,\dfrac 76,\dfrac 76)$, $(0,0,0)$, $(\dfrac 72,0,\dfrac 72)$; (2) $\dfrac{5\sqrt{3}}3$

000304
(1) 证明略; (2) $1$; (3) $(\dfrac 13,1)$

010721
(1) 证明略; (2) $\dfrac{\sqrt{51}}{17}$; (3) $\dfrac{\sqrt{41}}8$

000294
(1) 证明略; (2) $\arcsin \dfrac{\sqrt{10}}5$

030462
(1) 证明略; (2) $\dfrac{\sqrt{2}}3$

000305
(1) 证明略; (2) $\dfrac\pi 3$与$\dfrac{2\pi}3$

000299
(1) 证明略; (2) $\arccos \dfrac 23$

004096
(1) $\arcsin \dfrac{\sqrt{15}}5$; (2) $\arccos \dfrac{\sqrt{10}}5$

010730
$\arccos \dfrac{3\sqrt{10}}{10}$

004348
(1) $\arccos\dfrac{\sqrt{10}}{10}$; (2) $\dfrac{2\sqrt{33}}{11}$

004698
(1) 证明略; (2) $\arcsin \dfrac{4\sqrt{5}}{25}$

030472
(1) 证明略; (2) $\dfrac{\sqrt{15}}{5}$; (3) 存在, $\dfrac{PM}{PC}=\dfrac 13$

004243
(1) $\dfrac{\sqrt{21}}7$; (2) $\sqrt{2}$

000296
(1) 证明略; (2) $2$

030468
B