Question

If $z_1=1+i,z_2=-2+3i$ and $z_3=ai/3$ , where $i^2=-1$ are collinear then the value of $a$ is

• A. $-1$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is D $5$

$z_1=1+i,z_2=-2+3i,z_3=\frac{ai}{3}$

$z_1=(1,1),z_2=(-2,3),z_3=(0,\frac{a}{3})$

Slope of $z_1{z}_2=$ slope of $z_2{z}_3$

$\frac{3-1}{-2-1}=\frac{\frac{a}{3}-3}{0+2}$

$\frac{2}{-3}=\frac{\frac{a}{3}-3}{2}$

$\frac{-4}{3}+3=\frac{a}{3}$

$\frac{a-4}{a}=\frac{a}{3}$

$a=5$