Matematika

Pertanyaan

help me! tolong dibantu ya Kaka,mohon kerjasamanya
help me! tolong dibantu ya Kaka,mohon kerjasamanya

1 Jawaban

  • P(2, -1, -3), Q(-1, a, -11) dan R(4, -3, -2)
    PQ = q - p = (-1-2, a-(-1), -11-(-3)) = (-3, a + 1, -8)
    PR = r - p = (4-2, -3-(-1), -2-(-3)) = (2, -2, 1)
    => |PR| = √(2^2 + (-2)^2 + 1^2) = √(4 + 4 + 1) = √9 = 3

    Proyeksi vektor PQ pada PR = -4i + 4j - 2k
    (PQ.PR)/|PR|^2 . PR = -4i + 4j - 2k
    (-3(2) + (a + 1)(-2) + (-8)(1)) / 3^2 . PR = -4i + 4j - 2k
    (-6 - 2a - 2 - 8)/9 . PR = -4i + 4j - 2k
    (-16 - 2a)/9 (2i - 2j + k) = -4i + 4j - 2k
    (-16 - 2a)/9 (2i - 2j + k) = -2(2i - 2j + k)
    (-16 - 2a)/9 = -2
    -16 - 2a = -18
    -2a = -2
    a = 1