Last updated at May 6, 2021 by Teachoo

Transcript

Misc 9 Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are (2π β + π β) and (π β β 3π β) externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ. Given (ππ) β = 2π β + π β (ππ) β = π β β 3π β Since R divides PQ externally in the ratio 1 : 2 Position vector of R = (π Γ (πΆπΈ) β β π Γ (πΆπ·) β)/(π β π) (ππ ) β = (1(π β β 3π β ) β 2(2π β + π β))/(β1) = (π β β 3π β β 4π β β 2π β)/(β1) = (β3π β β 5π β )/(β1) = ππ β+ππ β Thus, position vector of R = (ππ ) β = 3π β+5π β Finding mid point of RQ Position vector of mid-point = ((ππ) β + (ππ ) β)/2 = (π β β 3π β + 3π β + 5π β)/2 = (4π β + 2π β)/2 = 2π β+π β This is the position vector of P. Thus, P is the mid point of RQ. Hence proved

Miscellaneous

Misc 1
Important

Misc 2

Misc 3 Important

Misc 4

Misc 5 Important

Misc 6

Misc 7 Important

Misc 8 Important

Misc 9 You are here

Misc 10 Important

Misc 11 Important

Misc 12 Important

Misc 13 Important

Misc 14 Important

Misc 15 Important

Misc 16 Important

Misc 17 Important

Misc 18 Important

Misc 19 Important

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.