16. If p, q, r are position vectors of the points P, Q R respectively, where p = a + 2b +5c, q = 3a + 2b + C, r=2a + 2b + 3c, then show that the points P, Q, R are collinear.
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Answer:
p
=
a
+2
b
+5
c
q
=3
a
+2
b
+
c
r
=2
a
+2
b
+3
c
P,Q,R are collinear if
p
+
q
=λ
r
⇒
a
+2
b
+5
c
+3
a
+2
b
+
c
=λ(2
a
+2
b
+3
c
)
⇒4
a
+4
b
+6
c
=2λ
a
+2λ
b
+3λ
c
⇒2λ=4,3λ=6
∴λ=2
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