Q10 of 35 Page 787

Show that the following points are collinear :

P(3, -2, 4), Q(1, 1, 1) and R(-1, 4, 2)


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,


Vertices should be R(-1, 4, -2)


The solution according is


(x1,y1,z1)= (3, -2, 4)


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


(x3,y3,z3)= (-1, 4,- 2)


Length PQ=


=


=


=


=


Length QR=


=


=


=


=


Length PR =


=


=


=


= = 2


PQ + QR= + =2 = PR


Therefore P, Q, R are collinear.



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