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Mathematics
Problem
The unit vector which is orthogonal to the vector
3
i
^
+
2
j
^
+
6
k
^
3\hat{i} + 2\hat{j} + 6\hat{k}
3
i
^
+
2
j
^
+
6
k
^
and is coplanar with the vectors
2
i
^
+
j
^
+
k
^
2\hat{i} + \hat{j} + \hat{k}
2
i
^
+
j
^
+
k
^
and
i
^
−
j
^
+
k
^
\hat{i} - \hat{j} + \hat{k}
i
^
−
j
^
+
k
^
is a.
2
i
^
−
6
j
^
+
k
^
41
\frac{2\hat{i} - 6\hat{j} + \hat{k}}{\sqrt{41}}
41
2
i
^
−
6
j
^
+
k
^
b.
2
i
^
−
3
j
^
13
\frac{2\hat{i} - 3\hat{j}}{\sqrt{13}}
13
2
i
^
−
3
j
^
c.
3
j
^
−
k
^
10
\frac{3\hat{j} - \hat{k}}{\sqrt{10}}
10
3
j
^
−
k
^
d.
4
i
^
+
3
j
^
−
3
k
^
34
\frac{4\hat{i} + 3\hat{j} - 3\hat{k}}{\sqrt{34}}
34
4
i
^
+
3
j
^
−
3
k
^
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