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Mathematics
Problem
If the vector
b
⃗
=
3
j
^
+
4
k
^
\vec{b} = 3\hat{j} + 4\hat{k}
b
=
3
j
^
+
4
k
^
is written as the sum of a vector
b
⃗
1
\vec{b}_1
b
1
, parallel to
a
⃗
=
i
^
+
j
^
\vec{a} = \hat{i} + \hat{j}
a
=
i
^
+
j
^
and a vector
b
⃗
2
\vec{b}_2
b
2
, perpendicular to
a
⃗
\vec{a}
a
, then
b
⃗
1
×
b
⃗
2
\vec{b}_1 \times \vec{b}_2
b
1
×
b
2
is equal to : (1)
−
6
i
^
+
6
j
^
−
9
2
k
^
-6\hat{i} + 6\hat{j} - \frac{9}{2}\hat{k}
−
6
i
^
+
6
j
^
−
2
9
k
^
(2)
−
3
i
^
+
3
j
^
−
9
k
^
-3\hat{i} + 3\hat{j} - 9\hat{k}
−
3
i
^
+
3
j
^
−
9
k
^
(3)
6
i
^
−
6
j
^
+
9
2
k
^
6\hat{i} - 6\hat{j} + \frac{9}{2}\hat{k}
6
i
^
−
6
j
^
+
2
9
k
^
(4)
3
i
^
−
3
j
^
+
9
k
^
3\hat{i} - 3\hat{j} + 9\hat{k}
3
i
^
−
3
j
^
+
9
k
^
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