Q. 10 B

# Show that the following points are collinear :A(3, -5, 1), B(-1, 0, 8) and C(7, -10, -6)

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)= (3, -5, 1)

(x2,y2,z2)= (-1, 0, 8)

(x3,y3,z3)= (7, -10, -6)

Length AB =

=

=

=

= = 3

Length BC =

=

=

=

= = 6

Length AC =

=

=

=

= = 3

BA + BC = 3 + 3 =6 = BC

Therefore A, B, C are collinear.

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