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| title | weight |
|---|---|
| Dot and cross products | 4 |
Author: John Wellbelove
Date: 2019
Dot Product
The dot product of two vectors is the sum of the products of the corresponding elements.
The dot product of vectors (x1, y1) and (x2, y2) is x1 * x2 + y1 * y2.
If A & B are vectors, the dot product is |A||B|cos(θ), where θ is the angle between the A and B.
|A| is the length of the vector A.
|B| is the length of the vector B.
Therefore, we can calculate cos(θ) = (A ⋅ B)/(|A||B|).
A dot product of 0 indicates two perpendicular lines, and the dot product is greatest when the lines are parallel.
Cross Product
The cross product of vectors (x1, y1) and (x2, y2) is x1 * y2 - y1 * x2
If A & B are vectors, the cross product is |A||B|sin(θ).
|θ| is the angle between the two vectors, but θ can be positive or negative.
Therefore, we can calculate sin(θ) = (A x B)/(|A||B|).