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Jawabannya c. -4

Jawaban terlampir di gambar

Kode : 12.2.4 [Kelas 12 Matematika BAB 4 - Vektor]

Penyelesaian

Titik-titik
A(3, -2, 4)
B(1, 3, -2)
C(x, 2, 4)

Vektor AC = vektor OC - vektor OA
[tex]AC = \left[\begin{array}{ccc}x\\2\\4\end{array}\right] - \left[\begin{array}{ccc}3\\-2\\4\end{array}\right][/tex]

[tex]AC = \left[\begin{array}{ccc}x-3\\4\\0\end{array}\right][/tex]

Vektor AB = vektor OB - vektor OA
[tex]AB = \left[\begin{array}{ccc}1\\3\\-2\end{array}\right] - \left[\begin{array}{ccc}3\\-2\\4\end{array}\right][/tex]

[tex]AB = \left[\begin{array}{ccc}-2\\5\\-6\end{array}\right][/tex]

|AC| = |AB|
[tex] \sqrt{(x-3)^2+4^2+0^2} = \sqrt{(-2)^2+5^2+(-6)^2} [/tex]
[tex] \sqrt{x^2-6x+9+16} = \sqrt{4+25+36} [/tex]
Kuadratkan kedua ruas
x² - 6x + 25 = 65
x² - 6x - 40 = 0
(x - 10)(x + 4) = 0
 
Diperoleh nilai x = -4 atau x = 10.
Jawaban yang tersedia adalah C. -4.