Q. 10 A4.3( 3 Votes )

Show that the following points are collinear :

A(-2, 3, 5), B(1, 2, 3) and C(7, 0, -1)

Answer :

To prove: the 3 points are collinear.


Formula:


The distance between two points (x1,y1,z1) and (x2,y2,z2) is given by


D=


Here,


(x1,y1,z1)= (-2, 3, 5)


(x2,y2,z2)= (1, 2, 3)


(x3,y3,z3)= (7, 0, -1)


Length AB =


=


=


=


=


Length BC =


=


=


=


= = 2


Length AC =


=


=


=


= = 3


AB + BC = + 2 =3 = AC


Therefore A, B, C are collinear.



Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Everything you need to know about OrthocentreEverything you need to know about OrthocentreEverything you need to know about Orthocentre46 mins
Interactive Quiz on Centroid, incentre, orthocentre & circumcentreInteractive Quiz on Centroid, incentre, orthocentre & circumcentreInteractive Quiz on Centroid, incentre, orthocentre & circumcentre56 mins
Know All About Centroid of Triangle & its PropertiesKnow All About Centroid of Triangle & its PropertiesKnow All About Centroid of Triangle & its Properties56 mins
Hybridisation, Shape & GeometryHybridisation, Shape & GeometryHybridisation, Shape & Geometry54 mins
Understand the Concept of LocusUnderstand the Concept of LocusUnderstand the Concept of Locus57 mins
Analyse Dimensional Analysis Through Live QuizAnalyse Dimensional Analysis Through Live QuizAnalyse Dimensional Analysis Through Live Quiz44 mins
Parametric Equations of Straight lineParametric Equations of Straight lineParametric Equations of Straight line48 mins
Interactive Quiz on Common tangents & angle of intersection of 2 circlesInteractive Quiz on Common tangents & angle of intersection of 2 circlesInteractive Quiz on Common tangents & angle of intersection of 2 circles56 mins
Standard Equation of CircleStandard Equation of CircleStandard Equation of Circle54 mins
Properties of normal of parabola | Interactive QuizProperties of normal of parabola | Interactive QuizProperties of normal of parabola | Interactive Quiz46 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses