diketahui titik P (2,3,-1) Q (5,2,3) dan R (-3,2,4) jika vektor p=PQ dan vektor q= QR, tentukan; a. p dan q b. proyeksi vektor ortogonal vektor p pada vektor q

Vektor


p = PQ = Q-P = (5 2 3)-(2 3 -1) = (3 -1 4)
q = QR = R-Q = (-3 2 4)-(5 2 3) = (-8 0 1)
..
p pada q :
= p . q / |q|² × q
= (3 -1 4)(-8 0 1) / (√-8²+0²+1²)² × (-8 0 1)
= -24+0+4 / 64+0+1 × (-8 0 1)
= -20/65 × (-8 0 1)
= -4/13 (-8 0 1)

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