Complex Numbers And Quadratic Equations question 349
Question: If $ z_1=1+i,z_2=-2+3iandz_3=ai/3 $ , where $ i^{2}=-1, $ are collinear then the value of a is [AMU 2001]
Options:
A) - 1
B) 3
C) 4
D) 5
Show Answer
Answer:
Correct Answer: D
Solution:
$ z_1=1+i\Rightarrow z_1=(1,1) $ $ z_2=-2+3i\Rightarrow z_2=(-2,3) $ $ z_3=\frac{ai}{3}\Rightarrow z_3=(0,a/3) $ $ \because z_1,z_2 $ and $ z_3 $ are collinear $ | \begin{matrix} 1 & 1 & 1 \\ -2 & 3 & 1 \\ 0 & a/3 & 1 \\ \end{matrix} |=0 $
Þ $ -\frac{a}{3}(1+2)+1(3+2)=0 $
Þ $ -a+5=0\Rightarrow a=5 $ .
BETA
