HASIL KALI SKALAR DUA VEKTOR

posted by missx on Mei 16, 2019 No Comments

Hasil gambar untuk VEKTORHasil kali skalar dua vektor

Selain rumus di R^3, ada rumus lain dalam hasil kali skalar dua vektor. Jika \bar{a} = a\bar{I} + a_2\bar{J} + a_3\bar{K} dan \bar{b} = b_1\bar{i} + b_2\bar{j} + b_3\bar{k} maka \bar{a}.\bar{b} adalah:
\bar{a}.\bar{b} = (a_1b_1) + (a_2b_2) + (a_3b_3)

Proyeksi Orthogonal vektor

Jika vektor \bar{a} diproyeksikan ke vektor bar{b} dan diberi nama \bar{c} seperti gambar dibawah:
proyeksi orthogonal vektor
Diketahui:
\bar{a}.\bar{b} = \mid\bar{a}\mid \mid \bar{b} \mid cos\theta \overset{maka}{\rightarrow} cos\theta = \frac{\bar{a}.\bar{b}}{\mid\bar{a}\mid\mid\bar{b}\mid}
Sehingga:
\mid\bar{c}\mid = \mid\bar{a}\mid\mid cos\theta\mid atau \mid\bar{c}\mid = \mid\frac{\bar{a}.\bar{b}}{\mid\bar{b}\mid}\mid
Untuk mendapat vektornya:
\bar{c} = \mid\frac{\bar{a}.\bar{b}}{\mid \bar{b} \mid} \mid \bar{b}

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