Let
be two vectors with real components:
Definition 29 a→⋅b→=a1b1+…+aNbN=∑j=1kajbj is called scalar product of a→ and b→Note: a→,b→∈RN,a→⋅b→∈R!!
Example:
Example from physics:Work:
now definitions for a→,b→∈RN
a→,b→≠0→. If a→⋅b→=0 then a→ is called orthogonal or perpendicular to b→ or a→⊥b→
a→⋅b→|a→||b→|≤1. We define cosφ=a→⋅b→|a→||b→| where φ is the angle between the two vectors a→ and b→ in R
a→=(1111)b→=(2200)⇒cosφ=2+2+0+048=12⇒φ=π4=45∘a→=(1111)b→=(1−1−11)⇒a→⋅b→=1−1−1+1=0→a→⊥b→
With frame
Scalar product
© J. Carstensen (Math for MS)