Question

Trong hệ trục tọa độ Oxy, cho \(\overrightarrow{A}=\left(1;2\right),\) \(\overrightarrow{B}=\left(3;-1\right)\) , \(\overrightarrow{C}=\left(5;6\right)\)

Hãy tìm cặp số (x,y) sao cho \(\overrightarrow{C}=x\cdot\overrightarrow{A}+y\cdot\overrightarrow{B}\)

a) tìm \(2.\overrightarrow{A}+3\cdot\overrightarrow{B}\)

b) Tìm \(\overrightarrow{A}\cdot\overrightarrow{B}=A_1\cdot B_1+A_2\cdot B_2\)

Giúp em nhé! Cảm ơn!

Answer 1

a: \(\Leftrightarrow\left\{{}\begin{matrix}x+3y=5\\2x-y=6\end{matrix}\right.\)=>x=23/7; y=4/7

b: \(2\cdot\overrightarrow{A}+3\cdot\overrightarrow{B}\)

\(=\left(2\cdot1+3\cdot3;2\cdot2+3\cdot\left(-1\right)\right)\)

=(11;1)

c: \(\overrightarrow{A}\cdot\overrightarrow{B}=\left(3;-2\right)\)