Perhatikan empat vektor berikut:
\begin{aligned} \vec{a} &= -\hat{i}+4\hat{j}+z\hat{k} \\[8pt] \vec{b} &= x\hat{i}-3\hat{j}+4\hat{k} \\[8pt] \vec{c} &= 2\hat{i}+y\hat{j}+8\hat{k} \\[8pt] \vec{d} &= -\hat{i}+6\hat{j}+3\hat{k} \end{aligned}
Jika \( \vec{a} \cdot \vec{b} = \vec{c} \cdot \vec{d} \), berapakah nilai \(2x+3y-z =\cdots \)
- -10
- -8
- -6
- 6
- 8
Pembahasan:
Karena \( \vec{a} \cdot \vec{b} = \vec{c} \cdot \vec{d} \), maka kita peroleh berikut:
\begin{aligned} \vec{a} \cdot \vec{b} &= \vec{c} \cdot \vec{d} \\[8pt] \begin{pmatrix} -1 \\ 4 \\ z \end{pmatrix} \cdot \begin{pmatrix} x \\ -3 \\ 4 \end{pmatrix} &= \begin{pmatrix} 2 \\ y \\ 8 \end{pmatrix} \begin{pmatrix} -1 \\ 6 \\ 3 \end{pmatrix} \\[8pt] \begin{pmatrix} -x \\ -12 \\ 4z \end{pmatrix} &= \begin{pmatrix} -2 \\ 6y \\ 24 \end{pmatrix} \\[8pt] -x &= -2 \Leftrightarrow x = 2 \\[8pt] -12 &= 6y \Leftrightarrow y = -2 \\[8pt] 4z &= 24 \Leftrightarrow z = 6 \\[8pt] 2x+3y-z &= 2(2)+3(-2)-6 \\[8pt] &= 4-6-6 \\[8pt] &= -8 \end{aligned}
Jawaban B.
Oleh Tju Ji Long · Statistisi