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Mathematics
Problem
Let
a
=
3
i
^
−
j
^
+
2
k
^
\mathbf{a}=3\hat i-\hat j+2\hat k
a
=
3
i
^
−
j
^
+
2
k
^
and
b
=
2
i
^
+
4
j
^
−
k
^
\mathbf{b}=2\hat i+4\hat j-\hat k
b
=
2
i
^
+
4
j
^
−
k
^
. Which of the following is a unit vector perpendicular to both
a
\mathbf{a}
a
and
b
\mathbf{b}
b
? a)
−
i
^
−
j
^
+
2
k
^
6
\displaystyle \frac{-\hat i-\hat j+2\hat k}{\sqrt6}
6
−
i
^
−
j
^
+
2
k
^
b)
−
i
^
+
j
^
+
2
k
^
14
\displaystyle \frac{-\hat i+\hat j+2\hat k}{\sqrt{14}}
14
−
i
^
+
j
^
+
2
k
^
c)
−
i
^
+
j
^
+
2
k
^
6
\displaystyle \frac{-\hat i+\hat j+2\hat k}{\sqrt6}
6
−
i
^
+
j
^
+
2
k
^
d)
5
i
^
+
3
j
^
+
k
^
35
\displaystyle \frac{5\hat i+3\hat j+\hat k}{\sqrt{35}}
35
5
i
^
+
3
j
^
+
k
^
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