Question

Tentukan vektor-vektor yg tegak lurus terhadap a=(1,1,0,1) b=(1,2,1,0) c=(0,1,2,2)
berikan minimal 2 contoh ? ? ?
terima kasih

Answer 1

Misal vektornya adalah d(w,x,y,z)

a.d = 0
(1,1,0,1).(w,x,y,z) = 0
w + x + z = 0
 z = -w - x.............................(1)

b.d = 0
(1,2,1,0).(w,x,y,z) = 0
w + 2x + y = 0
y = -w - 2x.............................(2)
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c.d = 0
(0,1,2,2).(w,x,y,z) = 0
x + 2y + 2z = 0...........................(3)

masukkan pers (1) dan (2) ke pers (3)
x + 2(-w - 2x) + 2(-w - x) = 0
x - 2w - 2x - 2w - 2x = 0
-5x - 4w = 0
5x = -4w
x = w.................(4)

masukkan (4) ke (2)
........(5)

masukkan (4) dan (1)


contoh 1, w = 5







d(5,-4,3,-1)


contoh 2, w = 10







d(10,-8,6,-2)