A) Vertices of a right angled triangle
B) Collinear
C) Vertices of an obtuse angled triangle
D) Vertices of an equilateral triangle
Correct Answer: B
Solution :
Let \[{{z}_{1}}=1+3i,{{z}_{2}}=5+i\] and \[{{z}_{3}}=3+2i\] Then area of triangle \[A=\frac{1}{2}\left| \begin{matrix} {{x}_{1}} & {{y}_{1}} & 1 \\ {{x}_{2}} & {{y}_{2}} & 1 \\ {{x}_{3}} & {{y}_{3}} & 1 \\ \end{matrix} \right|=\frac{1}{2}\left| \begin{matrix} 1 & 3 & 1 \\ 5 & 1 & 1 \\ 3 & 2 & 1 \\ \end{matrix} \right|=0\] Hence \[{{z}_{1}},{{z}_{2}}\] and \[{{z}_{3}}\] are collinear.
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