If the lines 2x + 3ay – 1 = 0 and 3x + 4y + 1 = 0 are mutually perpendicular, then the value of a will be2None of these
Question
If the lines 2x + 3ay – 1 = 0 and 3x + 4y + 1 = 0 are mutually perpendicular, then the value of a will be
2
None of these
Solution
The condition for two lines Ax + By + C = 0 and Px + Qy + R = 0 to be perpendicular is AP + BQ = 0.
Given the two lines are 2x + 3ay - 1 = 0 and 3x + 4y + 1 = 0.
Comparing these with the general equation of a line, we get:
A1 = 2, B1 = 3a for the first line and A2 = 3, B2 = 4 for the second line.
Substituting these values into the condition for perpendicularity:
A1 * A2 + B1 * B2 = 0
2 * 3 + 3a * 4 = 0
6 + 12a = 0
12a = -6
a = -6 / 12
a = -0.5
So, the value of a is -0.5.
Similar Questions
What equation of the line through point (2, 1) and perpendicular to the line through (-4, 1) and (3, -2)?
Check whether the three lines represented by the equations given below intersect at a commonpoint.2x + y - 1 = 04x + 3y + 5 = 05x + 4y + 8 = 0Show your work.
a (non-zero) vector perpendicular to both ⎛⎝⎜−1−50⎞⎠⎟(−1−50) and ⎛⎝⎜−4−13⎞⎠⎟(−4−13) is
Determine whether the pair of lines is parallel, perpendicular, or neither.3x - 4y = -38x + 6y = -3
Find the equation of a line that goes through the point ( - 3, - 1 ) and is perpendicular to the line: y = - 1 / 4x - 1.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.