Miscellaneous

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Last updated at May 6, 2021 by Teachoo

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