Step-by-step explanation:
Given lines
L1
( 1 - a) x - y = 1 ......i)
L2
6x + ay = 9 ....ii)
Slope of line I) Is
m1 = - ( x-coefficient) / ( y-coefficient)
= - ( 1 - a) / - 1
= 1 - a
Slope of line II) is
m2 = - (x-coefficient) / ( y-coefficient)
= - 6 / a
Now by the question
In 1st case
L1 and L2 are parallel so
m1 = m2
( 1 - a) = - 6 / a
a - a² = - 6
a² - a - 6 = 0
a² - ( 3 - 2 ) a - 6 = 0
a² - 3a + 2a - 6 =0
a ( a - 3 ) + 2 ( a - 3 ) = 0
(a - 3 ) ( a + 2) = 0
Either
a = 3 or a = - 2
Now in second case
L1 and L2 are perpendicular so
m1 * m2 = - 1
1 - a * - 6/ a = - 1
- 6 + 6a = - a
6a + a = 6
7a = 6
a = 6 / 7
The value of a are 3 , -2 and 6/7
Hope it will help :)❤