Q10 of 35 Page 787

Show that the following points are collinear :

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


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.



More from this chapter

All 35 →
8

Show that the points P(1, 3, 4), Q(-1, 6, 10), R(-7, 4, 7) and S(-5, 1, 1) are the vertices of a rhombus.

 9

Show that D(-1, 4, -3) is the circumcentre of triangle ABC with vertices A(3, 2, -5), B(-3. 8, -5) and C(-3, 2, 1).

 10

Show that the following points are collinear :

A(3, -5, 1), B(-1, 0, 8) and C(7, -10, -6)


 10

Show that the following points are collinear :

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