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| 1 | The Dot Product calculates the dot product of the two input vectors, and outputs a [[number]]. |
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| 2 | ||
| 3 | The dot product is written using a central dot: |
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| 4 | ||
| 5 | A · B |
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| 6 | ||
| 7 | This means the dot product of the vectors A and B. |
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| 8 | ||
| 9 | [[/uploads/Dot Product.png]] |
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| 10 | ||
| 11 | ## Details |
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| 12 | ||
| 1 | 13 | The Dot Product is a way of multiplying two vectors together. |
| 2 | 14 | |
| 3 | 15 | We can calculate the Dot Product of two vectors this way: |
| ... | ... | @@ -6,7 +18,7 @@ A · B = \|A\| × \|B\| × cos(θ) |
| 6 | 18 | |
| 7 | 19 | Where \|A\| is the magnitude (length) of vector A, \|B\| is the magnitude (length) of vector B, and θ is the angle between A and B. |
| 8 | 20 | |
| 9 | So we multiply the length of A times the length of B, then multiply by the [[cosine|Cos]] of the angle between A and B. |
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| 21 | So we multiply the length of A times the length of B, then multiply by the cosine of the angle between A and B. |
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| 10 | 22 | |
| 11 | 23 | We can also calculate it algebraically this way: |
| 12 | 24 | |
| ... | ... | @@ -16,9 +28,7 @@ So we multiply the x's, multiply the y's, multiply the z's, and then sum them al |
| 16 | 28 | |
| 17 | 29 | The result is a [[number]] (called a "scalar" so we know it's not a vector). |
| 18 | 30 | |
| 19 | [[/uploads/Dot Product.png]] |
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| 20 | ||
| 21 | ## Right Angles |
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| 31 | ### Right Angles |
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| 22 | 32 | |
| 23 | 33 | When two vectors are at right angles to each other the dot product is zero. This can be a handy way of checking if two vectors are perpendicular. |
| 24 | 34 |