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CBSE Class 12 Maths 2010 Solved Paper

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Question : 17
Total: 29
Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are (2
→
a
+
→
b
) and (
→
a
−3
→
b
) respectively, externally in the ratio 1:2. Also, show that P is the midpoint of the line segment R.
Solution:  
Position vector of P is e (2
→
a
+
→
b
)
Position vector of point Q is (
→
a
−3
→
b
)
Point R divides the line segment PQ externally in a ratio of 1 : 2.
Position vector of R =
1(
→
a
−3
→
b
)−2(2
→
a
+
→
b
)
1−2
=
→
a
−3
→
b
−4
→
a
−2
→
b
1−2
 = 3
→
a
+5
→
b
Now, we need to show that P is the mid-point of RQ.
So, Position vector of P =
Point‌vector‌of‌R+Position‌vector‌of‌q
2

=
(3
→
a
+5
→
b
)+(
→
a
−3
→
b
)
2
 = (2
→
a
+
→
b
) = Position vector of P (given)
Hence proved.
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