In Vector Multiplications why Dot product uses cosine and Cross product uses sin ?
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You can’t really explain vector products to a 5 year old, but here’s the best I can do without pictures.
The sine and cosine functions describe the motion of a point rotating around the origin counterclockwise, with respect to the angle to the x axis. Cosine gives the x coordinate and sine gives the y coordinate.
Take your two vectors, and move and rotate the picture so that they start at the origin and one of them points to the right along the x axis.
The dot product is the position of one vector projected perpendicularly onto the other, times the length of the other vector. But projecting the non-x-axis vector onto the x axis is the same as just taking its x coordinate. Since cosine tracks the x coordinate, there’s a cosine in the formula.
The cross product is the area of the parallelogram formed by the vectors. Parallelogram area is base times height. But the height is just the y coordinate of the top of the non-x-axis vector, which is given by its length times the sine of the angle.
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