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Mathematics
Mathematics
Problem
Let
a
=
2
i
^
+
j
^
+
k
^
\mathbf{a} = 2\hat{i} + \hat{j} + \hat{k}
a
=
2
i
^
+
j
^
+
k
^
,
b
=
i
^
+
2
j
^
−
k
^
\mathbf{b} = \hat{i} + 2\hat{j} - \hat{k}
b
=
i
^
+
2
j
^
−
k
^
and
c
\mathbf{c}
c
is a unit vector coplanar to them. If
c
\mathbf{c}
c
is perpendicular to
a
\mathbf{a}
a
, then
c
\mathbf{c}
c
is equal to a.
1
2
(
−
j
^
+
k
^
)
\frac{1}{\sqrt{2}}(-\hat{j} + \hat{k})
2
1
(
−
j
^
+
k
^
)
b.
−
1
3
(
i
^
+
j
^
+
k
^
)
-\frac{1}{\sqrt{3}}(\hat{i} + \hat{j} + \hat{k})
−
3
1
(
i
^
+
j
^
+
k
^
)
c.
1
5
(
i
^
−
2
j
^
)
\frac{1}{\sqrt{5}}(\hat{i} - 2\hat{j})
5
1
(
i
^
−
2
j
^
)
d.
1
3
(
i
^
+
j
^
+
k
^
)
\frac{1}{\sqrt{3}}(\hat{i} + \hat{j} + \hat{k})
3
1
(
i
^
+
j
^
+
k
^
)
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