Answer:
a) \(k=-\frac{10}{3}\)
b) \(k=\frac{6}{5}\)
Step-by-step explanation:
If two lines \(y = m_1x+c_1\) and \(y=m_2x+c_2\) ( where, \(m_1\) and \(m_2\) are their slope respectively ) are,
Parallel, if,
\(m_1=m_2\)
Perpendicular, if,
\(m_1\times m_2 = -1\)
Here, the lines are,
3x - 5y = 9 ⇒ 5y = 3x - 9 ⇒ \(y=\frac{3}{5}x-\frac{9}{5}\)
2x + ky = 11 ⇒ ky = -2x + 11 ⇒ \(y=-\frac{2}{k}x + 11\)
a) If they are parallel,
\(\frac{3}{5}=-\frac{2}{k}\implies 3k=-10\implies k=-\frac{10}{3}\)
b) If they are perpendicular,
\(\frac{3}{5}\times -\frac{2}{k}=-1\implies -\frac{6}{5k}=-1\implies k=\frac{6}{5}\)
