Jika \( \vec{p} = \hat{i}-2\hat{j}+2\hat{k} \) dan \( \vec{q} = 3\hat{i}+6\hat{j}+2\hat{k} \), maka panjang vektor \( \vec{p}+\vec{q} = \cdots \)
- \( 4 \sqrt{3} \)
- \( 3 \sqrt{6} \)
- \( \sqrt{21} \)
- \( 10 \)
- \( 3 \sqrt{5} \)
Pembahasan:
Panjang vektor \( \vec{p}+\vec{q} \) dapat diperoleh sebagai berikut:
\begin{aligned} \vec{p}+\vec{q} &= (\hat{i}-2\hat{j}+2\hat{k})+(3\hat{i}+6\hat{j}+2\hat{k}) \\[8pt] &= (1+3)\hat{i}+(-2+6)\hat{j}+(2+2)\hat{k} \\[8pt] &= 4\hat{i}+4\hat{j}+4\hat{k} \\[8pt] |\vec{p}+\vec{q}| &= \sqrt{4^2+4^2+4^2} = \sqrt{16+16+16} \\[8pt] &= \sqrt{48} = 4\sqrt{3} \end{aligned}
Jawaban A.