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Mathematics
Problem
If
a
⃗
=
a
1
i
^
+
a
2
j
^
+
a
3
k
^
\vec{a} = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k}
a
=
a
1
i
^
+
a
2
j
^
+
a
3
k
^
and
b
⃗
=
b
1
i
^
+
b
2
j
^
+
b
3
k
^
\vec{b} = b_1 \hat{i} + b_2 \hat{j} + b_3 \hat{k}
b
=
b
1
i
^
+
b
2
j
^
+
b
3
k
^
then prove that
a
⃗
⋅
b
⃗
=
(
a
1
b
1
+
a
2
b
2
+
a
3
b
3
)
.
\vec{a} \cdot \vec{b} = (a_1 b_1 + a_2 b_2 + a_3 b_3).
a
⋅
b
=
(
a
1
b
1
+
a
2
b
2
+
a
3
b
3
)
.
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