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184_notes:math_review [2018/05/17 13:35] – [Vector Notation] curdemma | 184_notes:math_review [2018/05/17 13:45] – [Vector Addition] curdemma | ||
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$$\vec{a} = |\vec{a}|\hat{a}$$ | $$\vec{a} = |\vec{a}|\hat{a}$$ | ||
- | We also use unit vectors to describe the x, y, and z coordinate directions. | + | We also use unit vectors to describe the x, y, and z coordinate directions. |
$$\vec{a} = a_x\hat{x}+a_y\hat{y}+a_z\hat{z}$$ | $$\vec{a} = a_x\hat{x}+a_y\hat{y}+a_z\hat{z}$$ | ||
$$\vec{a} = a_x\hat{i}+a_y\hat{j}+a_z\hat{k}$$ | $$\vec{a} = a_x\hat{i}+a_y\hat{j}+a_z\hat{k}$$ | ||
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==== Vector Addition ==== | ==== Vector Addition ==== | ||
- | {{ course_planning: | + | [{{ course_planning: |
- | {{ course_planning: | + | [{{ course_planning: |
Two vectors are added (or subtracted) component by component: | Two vectors are added (or subtracted) component by component: | ||
$$ \vec{a} +\vec{b} = \langle a_x, a_y, a_z \rangle + \langle b_x, b_y, b_z \rangle = \langle a_x+b_x, a_y+b_y, a_z+b_z \rangle | $$ \vec{a} +\vec{b} = \langle a_x, a_y, a_z \rangle + \langle b_x, b_y, b_z \rangle = \langle a_x+b_x, a_y+b_y, a_z+b_z \rangle | ||
$$ \vec{a} - \vec{b} = \langle a_x, a_y, a_z \rangle - \langle b_x, b_y, b_z \rangle = \langle a_x-b_x, a_y-b_y, a_z-b_z \rangle $$ | $$ \vec{a} - \vec{b} = \langle a_x, a_y, a_z \rangle - \langle b_x, b_y, b_z \rangle = \langle a_x-b_x, a_y-b_y, a_z-b_z \rangle $$ | ||
//**Note: You CANNOT simply add or subtract the magnitudes.**// | //**Note: You CANNOT simply add or subtract the magnitudes.**// | ||
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==== Vector Multiplication ==== | ==== Vector Multiplication ==== | ||
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There are a couple of ways to calculate the dot product: | There are a couple of ways to calculate the dot product: | ||
- | {{ 184_notes: | + | [{{ 184_notes: |
- | {{ 184_notes: | + | [{{ 184_notes: |
- **Using vector components** - If you have two vectors given by $\vec{a}=\langle a_x, a_y, a_z \rangle$ and $\vec{b}=\langle b_x, b_y, b_z\rangle$, | - **Using vector components** - If you have two vectors given by $\vec{a}=\langle a_x, a_y, a_z \rangle$ and $\vec{b}=\langle b_x, b_y, b_z\rangle$, | ||
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=== Cross Product === | === Cross Product === | ||
- | {{ 184_notes: | + | [{{ 184_notes: |
- | {{ 184_notes: | + | [{{ 184_notes: |
The cross product is another way to " | The cross product is another way to " |