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Statements
𝐚
×
𝐛
=
|
𝐢
𝐣
𝐤
a
1
a
2
a
3
b
1
b
2
b
3
|
=
(
a
2
b
3
-
a
3
b
2
)
𝐢
+
(
a
3
b
1
-
a
1
b
3
)
𝐣
+
(
a
1
b
2
-
a
2
b
1
)
𝐤
=
∥
𝐚
∥
∥
𝐛
∥
(
sin
θ
)
𝐧
,
𝐚
𝐛
𝐢
𝐣
𝐤
subscript
𝑎
1
subscript
𝑎
2
subscript
𝑎
3
subscript
𝑏
1
subscript
𝑏
2
subscript
𝑏
3
subscript
𝑎
2
subscript
𝑏
3
subscript
𝑎
3
subscript
𝑏
2
𝐢
subscript
𝑎
3
subscript
𝑏
1
subscript
𝑎
1
subscript
𝑏
3
𝐣
subscript
𝑎
1
subscript
𝑏
2
subscript
𝑎
2
subscript
𝑏
1
𝐤
norm
𝐚
norm
𝐛
𝜃
𝐧
{\displaystyle{\displaystyle\mathbf{a}\times\mathbf{b}=\begin{vmatrix}\mathbf{%
i}&\mathbf{j}&\mathbf{k}\\
a_{1}&a_{2}&a_{3}\\
b_{1}&b_{2}&b_{3}\end{vmatrix}\\
=(a_{2}b_{3}-a_{3}b_{2})\mathbf{i}+(a_{3}b_{1}-a_{1}b_{3})\mathbf{j}+(a_{1}b_{%
2}-a_{2}b_{1})\mathbf{k}\\
=\|\mathbf{a}\|\|\mathbf{b}\|(\sin\theta)\mathbf{n},}}
det
{\displaystyle{\displaystyle\det}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
θ
𝜃
{\displaystyle{\displaystyle\theta}}
𝐢
𝐢
{\displaystyle{\displaystyle\mathbf{i}}}
𝐣
𝐣
{\displaystyle{\displaystyle\mathbf{j}}}
𝐤
𝐤
{\displaystyle{\displaystyle\mathbf{k}}}
Identifiers
