벡터와 공간 | 벡터의 내적

Vector dot product and vector length

• Both of them, scalar!

Proving vector dot product properties

• Commutative & Associative & Distributive

Proof of the Caushy-Swarz inequality

Vector triangle inequality

• Constant c is a positive!

Define angle between vectors

• Using by law of cosine and triangle properties
• "Perpendicular" means dot product of a vec and b vec, especially non-zero vector, is 0
• "Orthogonal" means dot product of a vec and b vec, even if zero vector, is also 0

Define plane in R3 with point & normal vector

• We can represent the plane by using components of normal vector and one point which is in the plane, like Ax+By+Cz=D formula