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KEAM 2012 Math Paper
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© examsiri.com
Question :
87 of 120
Marks:
+1
,
-0
If the vectors
3
⋀
i
−
4
⋀
j
−
⋀
k
and
2
⋀
i
+
3
⋀
j
−
6
⋀
k
represent the diagonals of a rhombus, then the length of the side of the rhombus is
15
15
√
3
5
√
3
2
15
√
3
2
17
√
3
2
Validate
Solution:
Given,
A
C
=
3
i
−
4
j
−
k
and
B
D
=
2
i
+
3
j
−
6
k
Let sides of a rhombus be
a
and
b
.
In
∆
A
B
C
,
A
C
=
A
B
+
B
C
⇒
3
i
−
4
j
−
k
=
a
+
b
̣.....(i)
∴
B
D
=
B
A
+
A
D
⇒
2
i
+
3
j
−
6
k
=
−
a
+
b
......(ii)
On adding Eqs. (i) and (ii), we get
5
i
−
j
−
7
k
=
2
b
⇒
|
2
b
|
=
√
5
2
+
1
2
+
7
2
⇒
|
b
|
=
√
25
+
1
+
49
2
⇒
|
b
|
=
√
75
2
=
5
√
3
2
© examsiri.com
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