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Mathematics
Mathematics
Problem
The position vectors of the vertices
A
A
A
,
B
B
B
and
C
C
C
of a triangle are
2
i
^
−
3
j
^
+
3
k
^
2\hat{i} - 3\hat{j} + 3\hat{k}
2
i
^
−
3
j
^
+
3
k
^
,
2
i
^
+
2
j
^
+
3
k
^
2\hat{i} + 2\hat{j} + 3\hat{k}
2
i
^
+
2
j
^
+
3
k
^
and
−
i
^
+
j
^
+
3
k
^
-\hat{i} + \hat{j} + 3\hat{k}
−
i
^
+
j
^
+
3
k
^
respectively. Let
l
l
l
denotes the length of the angle bisector
A
D
AD
A
D
of
∠
B
A
C
\angle BAC
∠
B
A
C
where
D
D
D
is on the line segment
B
C
BC
B
C
, then
2
l
2
2l^2
2
l
2
equals :
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