(2,3,-4),(-1,0,5),(3,4,-7) show that the set of points are collinear - Maths -

Question

(2,3,-4),(-1,0,5),(3,4,-7) show that the set of points are
collinear

Neha Sethi · Accepted Answer

Let the points be  A(2,3,-4),B(-1,0,5),C(3,4,-7) Three points A,B and C are collinear if direction ratios of AB and BC are proportional
Direction ratios of AB=-1-2,0-3,5-(-4)=-3,-3,9Direction ratios of BC=3-(-1),4-0,-7-5=4,4,-12So, a1=-3,b1=-3 and c1=9and a2=4,b2=4 and c2=-12Now,a2a1=-43b2b1=-43c2c1=-129=-43Since, a2a1=b2b1=c2c1=-43Therefore, A,B and C are collinear
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