a) Đúng. $\overset{\rightarrow}{u} = (a;b;c)$, $\left| \overset{\rightarrow}{u} \right| = 1$, $\overset{\rightarrow}{i} \in (1;0;1)$.

$\left. \cos(\overset{\rightarrow}{u},\overset{\rightarrow}{i}) = \dfrac{\overset{\rightarrow}{u} \cdot \overset{\rightarrow}{i}}{\left| \overset{\rightarrow}{u} \right|.\left| \overset{\rightarrow}{i} \right|} = \dfrac{a}{1.1} = a\Rightarrow a = \cos 60^{o} \right.$.

b) Sai. $a = \cos 60^{o} = \dfrac{1}{2}$.

Tương tự ta có $\left. b = \cos 60^{o} = \dfrac{1}{2};c = \cos 45^{o} = \dfrac{\sqrt{2}}{2}\Rightarrow\overset{\rightarrow}{u}\left( {\dfrac{1}{2},\dfrac{1}{2},\dfrac{\sqrt{2}}{2}} \right) \right.$.

$\left. \Rightarrow AB:\dfrac{x - 4}{1} = \dfrac{y - 4}{1} = \dfrac{z}{\sqrt{2}} \right.$.

c) Sai. $v(t) = \beta t + 300$, sau 2 giây, hạt đi được quãng đường là:

$\left. S = {\int_{0}^{2}{(\beta t + 300)}}dt = 608\Rightarrow 2\beta + 600 = 608\Rightarrow\beta = 4\text{~(Sai)} \right.$

d) Đúng. Sau 5 giây, hạt đi được quãng đường là:

$AB = {\int_{0}^{5}{(4t + 300)dt}} = 1550$.

$\left. \overset{\rightarrow}{AB} = k\overset{\rightarrow}{u}\Rightarrow\overset{\rightarrow}{AB} = k.\left| \overset{\rightarrow}{u} \right| = k.\sqrt{\dfrac{1}{4} + \dfrac{1}{4} + \dfrac{1}{2}} = k\Rightarrow k = 1550 \right.$.

$\left. \Rightarrow\overset{\rightarrow}{AB} = \left( {\dfrac{1500}{2};\dfrac{1500}{2};\dfrac{1500}{\sqrt{2}}} \right) \right.$.

$\left. \Rightarrow x_{B} = \dfrac{1500}{2} + x_{A} = \dfrac{1500}{2} + 4 = 779 \right.$.