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Question

The points A(2,3,5),B(1,2,3)andC(7,0,1) are _____


A

Collinear

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B

Vertex of equilateral triangle

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C

vertex of right angle triangle

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D

vertex of right angled isosceles triangle

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Solution

The correct option is A

Collinear


Let A (2,3,5)

B (1,2,3)

C (7,0,1)

AB = (1+2)2 + (23)2 + (35)2 = 9+1+4 = 14

BC = (71)2 + (02)2 + (13)2 = 36+4+16 = 214

AC = (7+2)2 + (03)2 + (15)2 = 81+9+36 = 314

Thus AB+BC=Ac

Hence points A,B,C are collinear and B lies between A & C


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