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Mathematics
Problem
Let
a
⃗
=
i
^
+
j
^
+
k
^
\vec{a} = \hat{i} + \hat{j} + \hat{k}
a
=
i
^
+
j
^
+
k
^
,
b
⃗
=
i
^
−
j
^
+
k
^
\vec{b} = \hat{i} - \hat{j} + \hat{k}
b
=
i
^
−
j
^
+
k
^
and
c
⃗
=
i
^
−
j
^
−
k
^
\vec{c} = \hat{i} - \hat{j} - \hat{k}
c
=
i
^
−
j
^
−
k
^
be three vectors. A vector
v
⃗
\vec{v}
v
in the plane of
a
⃗
\vec{a}
a
and
b
⃗
\vec{b}
b
, whose projection on
c
⃗
\vec{c}
c
is
1
3
\frac{1}{\sqrt{3}}
3
1
, is given by a.
i
^
−
3
j
^
+
3
k
^
\hat{i} - 3\hat{j} + 3\hat{k}
i
^
−
3
j
^
+
3
k
^
b.
−
3
i
^
−
3
j
^
−
k
^
-3\hat{i} - 3\hat{j} - \hat{k}
−
3
i
^
−
3
j
^
−
k
^
c.
3
i
^
−
j
^
+
3
k
^
3\hat{i} - \hat{j} + 3\hat{k}
3
i
^
−
j
^
+
3
k
^
d.
i
^
+
3
j
^
−
3
k
^
\hat{i} + 3\hat{j} - 3\hat{k}
i
^
+
3
j
^
−
3
k
^
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