Lecture 002

Vectors in \mathbb{R}^2

Initial Point: init point of vector Terminal Point: end of vector Notation: \overrightarrow{u}, \overrightarrow{v}, \overrightarrow{w}

Vector Addition: \overrightarrow{u} + \overrightarrow{v} = \langle{x_1 + x_2, y_1 + y_2}\rangle Scalar Multiplication: k \times \overrightarrow{v} = <kx, ky> where \overrightarrow{v} = (x, y) Magnitude: magnitude of \|v\| = \sqrt[2]{v_x^2 + v_y^2}

Vectors in \mathbb{R}^3

Z-axis: always pointing out from the paper (blue in \langle{r, g, b}\rangle) Standard Equation of a Sphere (surface only): a sphere centered at (a, b, c) with radius r is (x-a)^2 + (y-b)^2 + (z-c)^2 = r^2

unit vector: vector with magnitude 1

normalize vector: divide by its magnitude

vector in component form: \langle{x, y, z}\rangle express using standard unit vector: i, j, k, 0

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