6. Vector Operations

6.1. Vector Addition

[𝑥1𝑥2𝑥3]+[𝑦1𝑦2𝑦3]=[𝑥1+𝑦1𝑥2+𝑦2𝑥3+𝑦3]
Example
𝑎⃗=[6−2]𝑏⃗=[−44]𝑎⃗+𝑏⃗=[6+−4−2+4]=[22]

6.2. Vector Subtraction

[𝑥1𝑥2𝑥3]−[𝑦1𝑦2𝑦3]=[𝑥1−𝑦1𝑥2−𝑦2𝑥3−𝑦3]
Example
𝑢⃗=[15]𝑣⃗=[51]𝑢⃗−𝑣⃗=[1−55−1]=[−44]

6.3. Scalar Multiplication

𝑐×[𝑥1𝑥2𝑥3]=[𝑐×𝑥1𝑐×𝑥2𝑐×𝑥3]
Example
𝑎⃗=[21]3𝑎⃗=3[21]=[3⋅23⋅1]=[63]
𝑎⃗=[21]−1𝑎⃗=−1[21]=[−1⋅2−1⋅1]=[−2−1]