| If the system of linear equations |
| \[2x+2ay+az=0\] |
| \[2x+3by+bz=0\] |
| \[2x+4cy+cz=0,\] |
| where \[a,\text{ }b,\text{ }c\,\in R\] are non-zero and distinct; has a non-zero solution, then |
| [JEE MAIN Held on 07-01-2020 Morning] |
A) \[\frac{1}{a},\frac{1}{b},\frac{1}{c}\] are in A.P.
B) a, b, c are in A.P.
C) a + b + c = 0
D) a, b, c are in G.P.
Correct Answer: A
Solution :
[a] For non-trivial solution, \[\Delta =0\]
\[\Rightarrow 2bc-3bc+a(b-c)+a(3c-2b)=0\] \[\Rightarrow -bc-ab+2ac=0\] \[ab+bc=2ac\] \[\frac{1}{c}+\frac{1}{a}=\frac{2}{b}\] a, b, c are in HP
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