Question

cho 3 vecto \(a=\left(2;3;-5\right)\), \(b=\left(0;-3;4\right)\), \(c=\left(-1;-2;0\right)\)

phân tích vecto u=(3;7;-14) qua 3 vecto a,b,c

Answer 1

Giả sử \(\overrightarrow{u}=x.\overrightarrow{a}+y\overrightarrow{.b}+z.\overrightarrow{c}\)

\(\Rightarrow\left(3;7;-14\right)=x\left(2;3;-5\right)+y\left(0;-3;4\right)+z\left(-1;-2;0\right)\)

\(\Rightarrow\left(3;7;-14\right)=\left(2x;3x;-5x\right)+\left(0;-3y;4y\right)+\left(-z;-2z;0\right)\)

\(\Rightarrow\left(3;7;-14\right)=\left(2x-z;3x-3y-2z;-5x+4y\right)\)

\(\Rightarrow\left\{{}\begin{matrix}2x-z=3\\3x-3y-2z=7\\-5x+4y=-14\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=2\\y=-1\\z=1\end{matrix}\right.\)

Vậy \(\overrightarrow{u}=2.\overrightarrow{a}-\overrightarrow{b}+\overrightarrow{c}\)