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184_notes:math_review [2017/08/24 16:01] – [Scientific Notation] tallpaul | 184_notes:math_review [2017/08/24 16:06] – [Vector Multiplication] tallpaul | ||
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*If you dot two vectors that are perfectly perpendicular, | *If you dot two vectors that are perfectly perpendicular, | ||
*If you dot two vectors that point directly opposite each other, you will get the // | *If you dot two vectors that point directly opposite each other, you will get the // | ||
- | *The order of the dot product does not matter. This means that $\vec{a} \cdot \vec{b}$ will give you the same answer as $\vec{b} \cdot \vec{a}$, that is, | + | *The order of the dot product does not matter. This means that $\vec{a} \bullet |
- | $$\vec{a}\cdot\vec{b} = \vec{b}\cdot\vec{a}$$ | + | $$\vec{a}\bullet\vec{b} = \vec{b}\bullet\vec{a}$$ |
There are a couple of ways to calculate the dot product: | There are a couple of ways to calculate the dot product: | ||
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- **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 $\vec{b}=\langle b_x, b_y, b_z\rangle$, | ||
- | $$\vec{a} \cdot \vec{b} = a_x b_x+a_y b_y+a_z b_z$$ | + | $$\vec{a} \bullet |
- **Using whole vectors and angles** - You can also calculate the dot product by using the magnitudes of the two vectors and the angle between them. Using this method, it is much easier to visualize taking the parallel part of one vector and multiplying by the other vector. It doesn' | - **Using whole vectors and angles** - You can also calculate the dot product by using the magnitudes of the two vectors and the angle between them. Using this method, it is much easier to visualize taking the parallel part of one vector and multiplying by the other vector. It doesn' | ||
- | $$\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| cos(\theta) = |\vec{a}|cos(\theta)|\vec{b}|$$ | + | $$\vec{a} \bullet |
=== Cross Product === | === Cross Product === |