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Mathematics
Problem
Let
a
⃗
=
3
i
^
+
2
j
^
+
2
k
^
\vec{a} = 3\hat{i} + 2\hat{j} + 2\hat{k}
a
=
3
i
^
+
2
j
^
+
2
k
^
and
b
⃗
=
i
^
+
2
j
^
−
2
k
^
\vec{b} = \hat{i} + 2\hat{j} - 2\hat{k}
b
=
i
^
+
2
j
^
−
2
k
^
be two vectors. If a vector perpendicular to both the vectors
a
⃗
+
b
⃗
\vec{a} + \vec{b}
a
+
b
and
a
⃗
−
b
⃗
\vec{a} - \vec{b}
a
−
b
has the magnitude 12 then one such vector is (1)
4
(
2
i
^
+
2
j
^
−
k
^
)
4(2\hat{i} + 2\hat{j} - \hat{k})
4
(
2
i
^
+
2
j
^
−
k
^
)
(2)
4
(
−
2
i
^
−
2
j
^
+
k
^
)
4(-2\hat{i} - 2\hat{j} + \hat{k})
4
(
−
2
i
^
−
2
j
^
+
k
^
)
(3)
4
(
2
i
^
−
2
j
^
−
k
^
)
4(2\hat{i} - 2\hat{j} - \hat{k})
4
(
2
i
^
−
2
j
^
−
k
^
)
(4)
4
(
2
i
^
+
2
j
^
+
k
^
)
4(2\hat{i} + 2\hat{j} + \hat{k})
4
(
2
i
^
+
2
j
^
+
k
^
)
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