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KEAM 2014 Math Paper
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© examsnet.com
Question : 3
Total: 120
If
⋀
i
+
⋀
j
,
⋀
j
+
⋀
k
,
⋀
i
+
⋀
k
are the position vectors of the vertices of a triangle ABC taken in order, then ∠A is equal to
π
2
π
5
π
6
π
4
π
3
Validate
Solution:
Let position vector of the vertices are
O
A
=
∧
i
+
∧
j
,
O
B
=
∧
j
+
∧
k
and
O
C
=
∧
i
+
∧
k
Now.
A
B
=
−
∧
i
+
∧
k
and
A
C
=
∧
k
−
∧
j
∴
cos
θ
=
(
A
B
)
⋅
(
A
C
)
|
A
B
|
|
A
C
|
=
(
−
∧
i
+
∧
k
)
⋅
(
∧
k
−
∧
j
)
√
1
2
+
1
2
√
1
2
+
1
2
=
(
∧
k
)
2
√
2
√
2
=
1
2
⇒
θ
=
π
3
© examsnet.com
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