CST 325

This week, we learned about how vectors and scalars are connected, how vectors are used to think about space, how different equations can represent surfaces, and how to create rays with implicit surfaces.

This week, we learned about vector operations and their history. In a vector is a displacement/oriented magnitude where an origin is not needed with a magnitude: the length of a segment. The Pythagorean theorem is used to calculate the magnitude. A unit vector is a vector with a hat and magnitude 1. In vector normalization, the unit vector v with a hat, is found by dividing the vector by the magnitude.

In vector addition, the x1 and y2 are added across and is commutative. In vector subtraction, they are subtracted across in the same way but they are anti-commutative. Vector multiplication by a scalar is multiplied across. In vector multiplication, there is no multiplication symbol because that is the cross product. In scalar division, you can divide by a scalar. In the vector dot product, the dot product of a and b is the sum of a*b. The vector cross product has a specific pattern that is hard to describe in words so it's better to see a picture example.