Advertisement
Advertisement
Last updated at Dec. 8, 2016 by Teachoo
Transcript
Misc 3 Find the angle between the lines whose direction ratios are a, b, c and b − c, c − a, a − b. Angle between the lines with direction ratios a1, b1, c1 and a2, b2, c2 is given by cos θ = 𝒂𝟏 𝒂𝟐 + 𝒃𝟏 𝒃𝟐 + 𝒄𝟏 𝒄𝟐 𝒂𝟏𝟐 + 𝒃𝟏𝟐 + 𝒄𝟏𝟐 𝒂𝟏𝟐 + 𝒃𝟏𝟐 + 𝒄𝟏𝟐 Given, 𝑎1 = 𝑎, 𝑏1 = 𝑏, c1 = c and 𝑎2 = 𝑏 − 𝑐, 𝑏2 = 𝑐 − 𝑎, c2 = a – b So, cos θ = 𝑎 𝑏 − 𝑐 + 𝑏 𝑐 − 𝑎 + 𝑐(𝑎 − 𝑏) 𝑎2 + 𝑏2 + 𝑐2 𝑏 − 𝑐2 + 𝐶 − 𝑎2 + 𝑎 − 𝑏2 = 𝑎𝑏 − 𝑎𝑐 + 𝑏𝑐 − 𝑎𝑏 + 𝑐𝑎 − 𝑏𝑐 𝑎2 + 𝑏2 + 𝑐2 𝑏2 + 𝑐2 − 2𝑏𝑐 + 𝑐2 + 𝑎2 − 2𝑐𝑎 + 𝑎2 + 𝑏2 − 2𝑎𝑏 = 0 ∴ cos θ = 0 So, θ = 90° Therefore, angle between the given pair of lines is 90°
Miscellaneous
Misc 2
Misc 3 Deleted for CBSE Board 2022 Exams You are here
Misc 4 Important
Misc 5 Important
Misc 6 Important
Misc 7
Misc 8 Important
Misc 9 Important
Misc 10
Misc 11 Important
Misc 12 Important
Misc 13 Important
Misc 14 Important
Misc 15 Important
Misc 16
Misc 17 Important
Misc 18 Important
Misc 19
Misc 20 Important
Misc 21 Important
Misc 22 (MCQ) Important
Misc 23 (MCQ) Important
Miscellaneous
About the Author