TS EAMCET · Maths · Straight Lines
The lines \(x-2 y+1=0,2 x-3 y-1=0\) and \(3 x-y+k=0\) are concurrent. The angle between the lines \(3 x-y+k=0\) and \(m x-3 y+6=0\) is \(45^{\circ}\). If \(m\) is an integer, then \(m-k=\)
- A \(-6\)
- B \(18\)
- C \(6\)
- D \(-18\)
Answer & Solution
Correct Answer
(C) \(6\)
Step-by-step Solution
Detailed explanation
\( \begin{vmatrix} 1 & -2 & 1 \\ 2 & -3 & -1 \\ 3 & -1 & k \end{vmatrix} = 0 \) \( 1(-3k-1) + 2(2k+3) + 1(-2+9) = 0 \) \( -3k-1+4k+6+7=0 \) \( k+12=0 \Rightarrow k=-12 \) \( m_1 = 3 \), \( m_2 = \frac{m}{3} \)…
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