Question:
The lines 3x + 4y = 12 and kx – 3y = 7 are perpendicular. Find the value of k.
रेखाएँ 3x + 4y = 12 और kx – 3y = 7 एक दूसरे के लंबवत हैं। k का मान ज्ञात कीजिए।
Options:
- a) 4
- b) – 4
- c) 3
- d) – 3
- a) 4
- b) – 4
- c) 3
- d) – 3
correct answer : a)
Explanation:
Slope of the first line (3x + 4y = 12): m1 = -3/4.
Slope of the second line (kx – 3y = 7): m2 = -k/(-3) = k/3.
Since the lines are perpendicular, m1 * m2 = -1:
(-3/4) * (k/3) = -1 => -k/4 = -1 => k = 4.
पहली रेखा (3x + 4y = 12) की ढाल: m1 = -3/4.
दूसरी रेखा (kx – 3y = 7) की ढाल: m2 = -k/(-3) = k/3.
चूंकि रेखाएं लंबवत हैं, इसलिए m1 * m2 = -1:
(-3/4) * (k/3) = -1 => -k/4 = -1 => k = 4.