TS EAMCET · Maths · Determinants
If \(\left|\begin{array}{lll}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{array}\right|=0\), then the lines \(a_i x+b_i y+c_i=0(i=1,2,3)\) represent
- A parallel lines if \(\frac{a_i}{a_j} \neq \frac{b_i}{b_j} \neq \frac{c_i}{c_j}(i \neq j)\)
- B coincident lines if \(\frac{a_i}{a_j}=\frac{b_i}{b_j}(i \neq j)\)
- C concurrent lines but not coincident if \(\frac{a_i}{a_j}=\frac{b_i}{b_j}=\frac{c_i}{c_j}(i \neq j)\)
- D concurrent lines if \(\frac{a_i}{a_j} \neq \frac{b_i}{b_j} \neq \frac{c_i}{c_j}(i \neq j)\)
Answer & Solution
Correct Answer
(D) concurrent lines if \(\frac{a_i}{a_j} \neq \frac{b_i}{b_j} \neq \frac{c_i}{c_j}(i \neq j)\)
Step-by-step Solution
Detailed explanation
Given, \(\left|\begin{array}{lll}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{array}\right|=0\) \(\Rightarrow\) lines may be concurrent or two pair of lines be parallel Now, if \(\quad \frac{a_i}{a_j} \neq \frac{b_i}{b_j} \neq \frac{c_i}{c_j}(i \neq j)\) then lines…
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