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Mathematics
Mathematics
Problem
Let
c
^
\hat{c}
c
^
be a unit vector coplanar with
a
=
i
^
−
j
^
+
2
k
^
a = \hat{i} - \hat{j} + 2\hat{k}
a
=
i
^
−
j
^
+
2
k
^
and
b
=
2
i
^
−
j
^
+
k
^
b = 2\hat{i} - \hat{j} + \hat{k}
b
=
2
i
^
−
j
^
+
k
^
such that
c
^
\hat{c}
c
^
is perpendicular to
a
a
a
. If
P
P
P
be the projection of
c
^
\hat{c}
c
^
along
b
b
b
, where
P
=
11
k
P = \frac{\sqrt{11}}{k}
P
=
k
11
then find
k
k
k
.
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