Show that the points A( 2, 0 ), B( −1, 3 ) and C( 4, −2 ) are collinear.
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hree points A,B,C are collinear if direction ratios of AB and BC are proportional.
A(2,3,4) and B(−1,−2,1)
Direction ratios =−1−2,−2−3,1−4
=−3,−5,−3
So, a
1
=−3,b
1
=−5,c
1
=−3
B(−1,−2,1) and C(5,8,7)
Direction ratios =5−(−1),8−(−2),7−1
=6,10,6
so, a
2
=6,b
2
=10,c
2
=6
Now,
a
1
a
2
=
−3
6
=−2
b
1
b
2
=
−5
10
=−2
c
1
c
2
=
−3
6
=−2
Since
a
1
a
2
=
b
1
b
2
=
c
1
c
2
=−2
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