Show that the points P( -1.5, 3 ), Q( 6,- 2 ), R(-3, 4) are collinear
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Answer:
Let point (−2,3,5),(1,2,3)and(7,0,−1) be denoted by P , Q , and R respectively.
by using distance formula d=
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
+(z
1
−z
1
)
2
Point P,Q and R are collinear if they lie on a line.
PQ=
(1+2)
2
+(2−3)
2
+(3−5)
2
=
(3)
2
+(−1)
2
+(−2)
2
=
9+1+4
=
14
QR=
(7−1)
2
+(0−2)
2
+(−1−3)
2
=
(6)
2
+(−2)
2
+(−4)
2
=
36+4+16
=2
14
PR=
(7+2)
2
+(0−3)
2
+(−1−5)
2
=
(9)
2
+(−3)
2
+(−6)
2
=
81+9+36
=3
14
Hence,
PQ+QR=RP
=
14
+2
14
=3
14
the point are collinear
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