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2583885
PRODUTO ESCALAR
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paulomt14@hotmail.com
paulomt13hotmail.com
paulo013@gmail.com
Mind Map by
Paulomt13
, updated more than 1 year ago
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Created by
Paulomt13
about 9 years ago
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Resource summary
PRODUTO ESCALAR
Propriedades do produto escalar
v.w = w.v
u.(v+w) = u.v + u.w
(kv).w = v.(kw) = k(v.w
v.v = |v| |v| = |v|²
|kv| = |k| |v|
|u.v| ≤ |u| |v|
|u+v| ≤ |u| + |v|
Ponto médio
M= (x1+x2, y1+y2, z1+z2)/2
Paralelismo de vetores
x1/x2 = y1/y2 (= α)
Módulo de um vetor
lvl = √x²+ y²
Distância entre 2 vetores
d(AD)=√(x2-x1)² + (y2-y1)²
Vetor unitário e seu versor
v/lvl
- v/lvl
Ângulo entre dois vetores
u.v = |u| |v| cos(α)
cos(α)= u.v /|u||v|
Vetores ortogonais ┴
u┴v se u.v = 0
Ângulos diretores e Cossenos diretores de um vetor
Lembrar do ângulos entre vetores
cos²α + cos²β+ cos²γ = 1
Paulo Henrique
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