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EAMCET Engineering 2007 Solved Paper
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© examsnet.com
Question : 116
Total: 160
The ratio in which
^
i
+
2
^
j
+
3
^
k
divides the join of
−
2
^
i
+
3
^
j
+
5
^
k
and
7
^
i
−
^
k
is
2
:
1
2
:
3
3
:
4
1
:
4
Validate
Solution:
Let the line joining the points with position vectors
−
2
^
i
+
3
^
j
+
5
^
k
and
7
^
i
−
^
k
be divide in the ratio
λ
:
1
by
^
i
+
2
^
j
+
3
^
k
.
∴
λ
(
7
^
i
−
^
k
)
+
(
−
2
^
i
+
3
^
j
+
5
^
k
)
λ
+
1
=
^
i
+
2
^
j
+
3
^
k
⇒
(
7
λ
−
2
)
^
i
+
3
^
j
+
(
5
−
λ
)
^
k
=
(
λ
+
1
)
^
i
+
2
(
λ
+
1
)
^
j
+
3
(
λ
+
1
)
^
k
On equating the coefficient of
^
i
, we get
7
λ
−
2
=
λ
+
1
λ
=
2
Hence, ratio
λ
:
1
=
2
:
1
.
© examsnet.com
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