Question

If $m_1,m_2,m_3,m_4$, are respectively the magnitudes of the vectors $\overline{a_1}=\overline{2i}-\overline{j}+\overline{k},\overline{a_2}=\overline{3i}-\overline{4j}-\overline{4k},\overline{a_3}=-\overline{i}+\overline{j}-\overline{k},\overline{a_4}=-\overline{i}+3\overline{j}+\overline{k}$, then the correct order of $m_1,m_2,m_3,m_4$ is

• A. $m_3<m_1<m_4<m_2$
• B. $m_3<m_1<m_2<m_4$
• C. $m_3<m_4<m_1<m_2$
• D. $m_3<m_4<m_2<m_1$

Answer 1

Answer: (A)

$m_3<m_1<m_4<m_2$

Calculate $m_1,m_2,m_3$ and $m_4$
$m_1=\sqrt{2^2+1+1}=\sqrt{6}$
$m_2=\sqrt{9+16+16}=\sqrt{41}$
$m_3=\sqrt{1+1+1}=\sqrt{3}$
$m_4=\sqrt{1+9+1}=\sqrt{11}$
Hence,$m_3<m_1<m_4<m_2$