Question

Given vectors a = (2, 6) and b = (-3, 4), find – 3 a +5b.
Write your answer in component form.

Answer 1

Answer:

$\huge\boxed{-3\overrightarrow{a}+5\overrightarrow{b}=\left<-21;\ 2\right>}$

Step-by-step explanation:

$\overrightarrow{a}=\left<2;\ 6\right>\\\\\overrightarrow{b}=\left<-3;\ 4\right>\\\\-3\overrightarrow{a}+5\overrightarrow{b}=-3\left<2;\ 6\right>+5\left<-3;\ 4\right>=\left<-3\cdot2;\ -3\cdot6\right>+\left<5\cdot(-3);\ 5\cdot4\right>\\\\=\left<-6;\ -18\right>+\left<-15;\ 20\right>=\left<-6+(-15);\ -18+20\right>=\left<-21;\ 2\right>$