Question

Se considera vectorii v1=2i+aj si v2=(a+3)i+2j determinati a>0

Answer 1

[tex]\text{Vectorii }\overrightarrow{v}=a_1\cdot \overrightarrow{i}+b_1\cdot \overrightarrow{j}\ \text{si}\ \overrightarrow{y}=a_2\cdot \overrightarrow{i}+b_2\cdot \overrightarrow{j}\text{ sunt coliniari}\\ \text{daca si numai daca }\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\\ \text{In cazul nostru vom avea:}\\ \dfrac{2}{a+3}=\dfrac{a}{2}\\ a^2+3a=4\\ a^2+3a-4=0\\ (a+4)(a-1)=0\Rightarrow a_1=1\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2=-4\ \textless \ 0(\text{nu convine})\\ \text{Deci a=1.}[/tex]