show that the three points a(1,-2,3) b(2,3,-4) c(0,-7,10) are collinear - Maths - Pair of Straight Lines

Question

show that the three points a(1,-2,3) b(2,3,-4) c(0,-7,10) are
collinear

Ankita Agarwal · Accepted Answer

Dear Student,

Given points are A1,-2,3 B2,3,-4 and C0,-7,10Points A,B and C will be collinear, if the sum of the lengths of two line-segments is equal to the third
AB = 2-12+3+22+-4-32 = 1+25+49= 75BC = 0-22+-7-32+10+42 = 4+100+196= 300 = 75×2×2 = 275CA = 1-02+-2+72+3-102 = 1+25+49 = 75Since, AB+CA = BC, the points A,B and C are collinear

Regards