Vektor-ektor \(u, v\) dan \(x\) tidak nol. Vektor \((u+v)\) tegak lurus \((u-x)\), jika… (SBMPTN 2014)
- \( |u+v|=|u-v| \)
- \( |v|=|x| \)
- \( u \cdot u = v \cdot v; \ v = -x \)
- \( u \cdot u = v \cdot v; \ v = x \)
- \( u \cdot v = v \cdot v \)
Pembahasan:
Diketahui vektor \((u+v)\) tegak lurus \((u-x)\), sehingga
\begin{aligned} (u+v) \cdot (u-x) &= 0 \\[8pt] u \cdot u-u\cdot x+u \cdot v-v \cdot x &= 0 \\[8pt] \text{Jika} \ v = x, \ \text{maka} \ u \cdot u- v \cdot v &= 0 \\[8pt] u \cdot u &= v \cdot v \end{aligned}
Jawaban D.