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Mathematics
Mathematics
Problem
Let
α
⃗
=
3
i
^
+
j
^
\vec{\alpha} = 3\hat{i} + \hat{j}
α
=
3
i
^
+
j
^
and
β
⃗
=
2
i
^
−
j
^
+
3
k
^
\vec{\beta} = 2\hat{i} - \hat{j} + 3\hat{k}
β
=
2
i
^
−
j
^
+
3
k
^
. If
β
⃗
=
β
⃗
1
−
β
⃗
2
\vec{\beta} = \vec{\beta}_1 - \vec{\beta}_2
β
=
β
1
−
β
2
, where
β
⃗
1
\vec{\beta}_1
β
1
is parallel to
α
⃗
\vec{\alpha}
α
and
β
⃗
2
\vec{\beta}_2
β
2
is perpendicular to
α
⃗
\vec{\alpha}
α
, then
β
⃗
1
×
β
⃗
2
\vec{\beta}_1 \times \vec{\beta}_2
β
1
×
β
2
is equal to : (1)
−
3
i
^
+
9
j
^
+
5
k
^
-3\hat{i} + 9\hat{j} + 5\hat{k}
−
3
i
^
+
9
j
^
+
5
k
^
(2)
3
i
^
−
9
j
^
−
5
k
^
3\hat{i} - 9\hat{j} - 5\hat{k}
3
i
^
−
9
j
^
−
5
k
^
(3)
1
2
(
−
3
i
^
+
9
j
^
+
5
k
^
)
\frac{1}{2}(-3\hat{i} + 9\hat{j} + 5\hat{k})
2
1
(
−
3
i
^
+
9
j
^
+
5
k
^
)
(4)
1
2
(
3
i
^
−
9
j
^
+
5
k
^
)
\frac{1}{2}(3\hat{i} - 9\hat{j} + 5\hat{k})
2
1
(
3
i
^
−
9
j
^
+
5
k
^
)
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