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