The correct answer is option (B):
-12
Let's analyze the problem. We are given two lines:
Line 1: 7x + 6y + 9 = 0
Line 2: ax + 14y + 8 = 0
We are told that these lines are perpendicular to each other. The condition for two lines to be perpendicular is that the product of their slopes is -1.
First, let's find the slopes of the given lines. We can rewrite the equations in the slope-intercept form (y = mx + c), where 'm' represents the slope.
For Line 1:
6y = -7x - 9
y = (-7/6)x - 9/6
The slope of Line 1 (m1) is -7/6.
For Line 2:
14y = -ax - 8
y = (-a/14)x - 8/14
The slope of Line 2 (m2) is -a/14.
Since the lines are perpendicular, we have:
m1 * m2 = -1
(-7/6) * (-a/14) = -1
Now, we solve for 'a':
(7a) / 84 = -1
7a = -84
a = -84 / 7
a = -12
Therefore, the value of 'a' is -12.