Matematika

Pertanyaan

Diketahui P = (a, 0, 3), Q = (0, 6, 5) dan R(2, 7, c). Agar vektor PQ tegak lurus pada QR, maka a - c =

1 Jawaban

  • PQ = Q - P
    = (0, 6, 5) - (a, 0, 3)
    = (-a, 6, 2)

    QR = R - Q
    = (2, 7, c) - (0, 6, 5)
    = (2, 1, c - 5)

    Tegak lurus, PQ . QR = 0
    (-a)(2) + (6)(1) + 2(c - 5) = 0
    -2a + 6 + 2c - 10 = 0
    -2a + 2c - 4 = 0
    -2a + 2c = 4
    ------------------ (รท -2)
    a - c = -2

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