Mathematics - Vector Question with Solution | TestHub

$$\begin{array}{rl}& ax+2by+3b+\lambda (bx-2ay-3a)=0\\ & \Rightarrow (a+b\lambda )x+(2b-2a\lambda )y+3b-3\lambda a=0\\ & a+b\lambda =0\Rightarrow \lambda =-a/b\\ & \Rightarrow ax+2by+3b-\frac{a}{b}(bx-2ay-3a)=0\\ & \Rightarrow ax+2by+3b-ax+\frac{2a^2}{b}y+\frac{3a^2}{b}=0\\ & y\left(2b+\frac{2a^2}{b}\right)+3b+\frac{3a^2}{b}=0\\ & y\left(\frac{2b^2+2a^2}{b}\right)=-\left(\frac{3b^2+3a^2}{b}\right)\\ & y=\frac{-3\left(a^2+b^2\right)}{2\left(b^2+a^2\right)}=\frac{-3}{2}\\ & \end{array}$$ $y=-\frac{3}{2}$ so it is $3/2$ units below $x$-axis.