Q. 10 B

# Show that the following points are collinear :

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

Answer :

To prove: the 3 points are collinear.

Formula:

The distance between two points (x_{1},y_{1},z_{1}) and (x_{2},y_{2},z_{2}) is given by

D=

Here,

(x_{1},y_{1},z_{1})= (3, -5, 1)

(x_{2},y_{2},z_{2})= (-1, 0, 8)

(x_{3},y_{3},z_{3})= (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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