If 5a-36-20 = with a, b, c as position vectors of the point A, B, C respectively, then find the
ratio in which point C divides the line segment AB
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Answer:
Let the ratio be λ:1
Position vector of point (C)
c
=
λ+1
λ
a
+
b
Put the value of
c
in 2
a
+3
b
−5
c
=0
2
a
+3
b
−5×(
λ+1
λ
a
+
b
)=0
⇒
(λ+1)
(λ+1)(2
a
+3
b
)−5λ
a
−5
b
=0
⇒2
a
λ+3
b
λ+2
a
+3
b
−5λ
a
−5
b
=0
⇒3
b
λ−3
a
λ+2
a
−2
b
=0
⇒3λ(
b
−
a
)=2
b
−2
a
⇒3λ=
(
b
−
a
)
2(
b
−
a
)
⇒
1
λ
=
2
3
hence the point C divides line segment AB in the ratio 2:3.
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