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Byju's Answer
Standard XII
Mathematics
Section Formula
If a , b ...
Question
If
→
a
,
→
b
are the vectors of A , B respectively, find the position vector of a point C. AB produced such that AC = 3AB and that a point D in BA produced such that BD = 2BA
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Solution
Let position vector of
C
=
→
c
Let position vector of
D
=
→
d
→
A
C
=
→
c
−
→
a
→
A
B
=
→
b
−
→
a
→
B
D
=
→
d
−
→
b
→
B
A
=
→
a
−
→
b
A
C
=
3
A
B
⇒
→
c
−
→
a
=
3
(
→
b
−
→
a
)
⇒
→
c
−
→
a
=
3
→
b
−
3
→
a
⇒
→
c
=
3
→
b
−
2
→
a
⇒
→
B
D
=
2
→
B
A
⇒
→
d
−
→
b
=
2
(
→
b
−
→
a
)
⇒
→
d
−
→
b
=
2
→
b
−
2
→
a
⇒
→
d
=
3
→
b
−
2
→
a
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Q.
If
a
,
→
b
→
are the position vectors of A, B respectively, find the position vector of a point C in AB produced such that AC = 3 AB and that a point D in BA produced such that BD = 2BA.