Vektörel izdüşüm

a' nın b (a1) üzerindeki izdüşümü ve a' nın b (a2)' den çıktısı.
Eğer 90° < θ ≤ 180° ise a1 b ye ters yönde olacaktır.

Bir a vektörünün sıfır olmayan bir b vektörü, a' nın b yönündeki vektör bileşeni veya vektör çözümü olarak da bilinir, üzerindeki veya üzerine vektörel izdişümü, a' nın b' ye paralel bir doğru üzerine ortogonal izdüşümüdür. b'ye paralel bu vektör şu şekilde tanımlanır:

skalerdir ve a' nın b üzerine skaler izdüşümü olarak adlandırılır. ise bir b yönünde birim vektördür. Skaler izdüşüm ise şu şekilde tanımlanır:

operatör · nokta çarpımı ifade eder, |a| sembolü a' nın uzunluğunu ve θ ise a ve b arasındaki açıyı ifade eder.

a' nın b' den çıktısı[1] a' nın b' ye ortogonal olan düzleme (hiperdüzlem olarak da bilinir) ortogonal izdüşümüdür. Hem a1 hem a2 vektör a' nın izdüşümlerdir ve toplamları a' ya eşittir, bu da aşağıda verilen çıktı tarafından vurgulanmıştır:

Ayrıca bakınız

Kaynakça

  1. ^ Perwass, G. (2009). Geometric Algebra With Applications in Engineering. s. 83. 

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