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Joint Entrance Examination
Mathematics
Vector Algebra
Question 33
Question 33 of 379
Medium
MCQ
Let
A
,
B
,
C
A, B, C
A
,
B
,
C
be three points in xy-plane, whose position vector are given by
3
i
^
+
j
^
,
i
^
+
3
j
^
\sqrt{3} \hat{i}+\hat{j}, \hat{i}+\sqrt{3} \hat{j}
3
i
^
+
j
^
,
i
^
+
3
j
^
and
a
i
^
+
(
1
−
a
)
j
^
a \hat{i}+(1-a) \hat{j}
a
i
^
+
(
1
−
a
)
j
^
respectively with respect to the origin O . If the distance of the point C from...
A
2
B
0
C
9
2
\frac{9}{2}
2
9
D
1
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Official solution
x
−
y
=
0
∣
a
(
1
−
a
)
2
∣
=
9
2
⇒
a
=
5
−
4
=
5
+
(
−
4
)
=
1
\begin{gathered} x-y=0 \\ |\frac{a(1-a)}{\sqrt{2}}|=\frac{9}{\sqrt{2}}\Rightarrow a=5-4 \\ =5+(-4)=1 \end{gathered}
x
−
y
=
0
∣
2
a
(
1
−
a
)
∣
=
2
9
⇒
a
=
5
−
4
=
5
+
(
−
4
)
=
1
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