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Joint Entrance Examination
Mathematics
3D Geometry
Question 80
Question 80 of 521
Medium
MCQ
Let
O
O
O
be the origin and the position vectors of
A
A
A
and
B
B
B
be
2
i
^
+
2
j
^
+
k
^
2\hat{i}+2\hat{j}+\hat{k}
2
i
^
+
2
j
^
+
k
^
and
2
i
^
+
4
j
^
+
4
k
^
2\hat{i}+4\hat{j}+4\hat{k}
2
i
^
+
4
j
^
+
4
k
^
respectively. If the internal bisector of
\angleAOB
\angleAOB
\angleAOB
meets the line
A
B
AB
A
B
at
C
C
C
, then the length of
O
C
OC
O
C
is
A
3
2
34
\frac{3}{2}\sqrt{\sqrt{34}}
2
3
34
B
2
3
31
\frac{2}{3}\sqrt{\sqrt{31}}
3
2
31
C
2
3
34
\frac{2}{3}\sqrt{\sqrt{34}}
3
2
34
D
3
2
31
\frac{3}{2}\sqrt{\sqrt{31}}
2
3
31
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Solutions · 1
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Official solution
O
C
=
136
3
=
2
34
3
OC=\frac{\sqrt{136}}{3}=\frac{2\sqrt{34}}{3}
O
C
=
3
136
=
3
2
34
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