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Mathematics
Mathematics
Problem
Let,
a
⃗
=
i
^
+
2
j
^
+
k
^
\vec{a} = \hat{i} + 2\hat{j} + \hat{k}
a
=
i
^
+
2
j
^
+
k
^
,
b
⃗
=
i
^
−
j
^
+
k
^
\vec{b} = \hat{i} - \hat{j} + \hat{k}
b
=
i
^
−
j
^
+
k
^
,
c
⃗
=
i
^
+
j
^
−
k
^
\vec{c} = \hat{i} + \hat{j} - \hat{k}
c
=
i
^
+
j
^
−
k
^
. A vector coplanar to
a
⃗
\vec{a}
a
and
b
⃗
\vec{b}
b
has a projection along
c
⃗
\vec{c}
c
of magnitude
1
3
\frac{1}{\sqrt{3}}
3
1
, then the vector is a.
4
i
^
−
j
^
+
4
k
^
4\hat{i} - \hat{j} + 4\hat{k}
4
i
^
−
j
^
+
4
k
^
b.
4
i
^
+
j
^
−
4
k
^
4\hat{i} + \hat{j} - 4\hat{k}
4
i
^
+
j
^
−
4
k
^
c.
2
i
^
+
j
^
+
k
^
2\hat{i} + \hat{j} + \hat{k}
2
i
^
+
j
^
+
k
^
d. None of these
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