题目
设向量overrightarrow(a)与向量overrightarrow(b)= ( (2,-1,2) )平行,并满足等式overrightarrow(a)cdot overrightarrow(b)=-18,则overrightarrow(a)=_ _ _ _ _ _ _ _ _ _ .
设向量$\overrightarrow{a}$与向量$\overrightarrow{b}=\left ( {2,-1,2} \right )$平行,并满足等式$\overrightarrow{a}\cdot \overrightarrow{b}=-18$,则$\overrightarrow{a}=$$\_ \_ \_ \_ \_ \_ \_ \_ \_ \_ $.
题目解答
答案
$\because \overrightarrow{a}\parallel \overrightarrow{b}$
$\therefore $设$\overrightarrow{a}=k\overrightarrow{b}$
$\because \overrightarrow{b}=\left ( {2,-1,2} \right )$
$\therefore \overrightarrow{a}=k\left ( {2,-1,2} \right )$
$=\left ( {2k,-k,2k} \right )$
$\because \overrightarrow{a}\cdot \overrightarrow{b}=-18$
$\therefore 2\times 2k+\left ( {-1} \right )\times \left ( {-k} \right )+2\times 2k=-18$
解得$k=-2$
$\therefore \overrightarrow{a}=\left ( {-4,2,-4} \right )$
综上所述,答案:$\left ( {-4,2,-4} \right )$