
Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Miscellaneous
Misc 2 Important
Misc 3 Important You are here
Misc 4 Important
Misc 5 Important
Question 1 Important Deleted for CBSE Board 2024 Exams
Question 2 Deleted for CBSE Board 2024 Exams
Question 3 Important Deleted for CBSE Board 2024 Exams
Question 4 Deleted for CBSE Board 2024 Exams
Question 5 Important Deleted for CBSE Board 2024 Exams
Question 6 Deleted for CBSE Board 2024 Exams
Question 7 Important Deleted for CBSE Board 2024 Exams
Question 8 Important Deleted for CBSE Board 2024 Exams
Question 9 Important Deleted for CBSE Board 2024 Exams
Question 10 Important Deleted for CBSE Board 2024 Exams
Question 11 Important Deleted for CBSE Board 2024 Exams
Question 12 Deleted for CBSE Board 2024 Exams
Question 13 Important Deleted for CBSE Board 2024 Exams
Question 14 Important Deleted for CBSE Board 2024 Exams
Question 15 Deleted for CBSE Board 2024 Exams
Question 16 Important Deleted for CBSE Board 2024 Exams
Question 17 (MCQ) Important Deleted for CBSE Board 2024 Exams
Question 18 (MCQ) Important Deleted for CBSE Board 2024 Exams
Miscellaneous
Last updated at Aug. 14, 2023 by Teachoo
Misc 3 If the lines (𝑥 − 1)/( − 3) = (𝑦 − 2)/2𝑘 = (𝑧 − 3)/2 and (𝑥 − 1)/3𝑘 = (𝑦 − 1)/1 = (𝑧 − 6)/( − 5) are perpendicular, find the value of k. Two lines (𝑥 − 𝑥1)/( 𝑎1) = (𝑦 −𝑦1)/𝑏1 = (𝑧 − 𝑧1)/𝑐1 and (𝑥 − 𝑥2)/( 𝑎2) = (𝑦 − 𝑦2)/𝑏2 = (𝑧 − 𝑧2)/𝑐2 are perpendicular to each other if 𝒂𝟏 𝒂𝟐 + 𝒃𝟏 𝒃𝟐 + 𝒄𝟏 𝒄𝟐 = 0 (𝒙 − 𝟏)/( − 𝟑) = (𝒚 − 𝟐)/( 𝟐𝒌) = (𝒛 − 𝟑)/( 𝟐) Comparing with (𝑥 − 𝑥1)/( 𝑎1) = (𝑦− 𝑦1)/( 𝑏1) = (𝑧− 𝑧1)/( 𝑐1) x1 = 1, y1 = 2, z1 = 3 & 𝒂𝟏 = −3, b1 = 2k c1 = 2 (𝒙 − 𝟏)/( 𝟑𝒌) = (𝒚 − 𝟏)/( 𝟏) = (𝒛 − 𝟔)/( − 𝟓) Comparing with (𝑥 − 𝑥2)/( 𝑎2) = (𝑦 − 𝑦2)/( 𝑏2) = (𝑧 − 𝑧2)/( 𝑐2), 𝑥2 = 1, y2 = 1, z2 = 6 & 𝒂𝟐 = 3k, b2 = 1, c2 = −5, Since the two lines are perpendicular, 𝑎1 𝑎2 + 𝑏1 𝑏2 + c1𝑐2 = 0 (−3 × 3k) + (2k × 1) + (2 × − 5) = 0 − 9k + 2k − 10 = 0 − 7k = 10 k = (−𝟏𝟎)/𝟕 Therefore, k = (−10)/7