Question

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

$m_3 < m_1 < m_4 < m_2$

Answer 2

Given, $m_1 = |a_1| = \sqrt{2^2 + -1^2 + 1^2} = \sqrt{6}$ $m_2 = |a_2| = \sqrt{3^2 + -4^2 + -4^2} = \sqrt{6}$ $m_3 = |a_3| = \sqrt{1^2 + 1^2 + -1^2} = \sqrt{3}$ and $m_4 = |a_4| = \sqrt{-1^2 + 3^2 + 1^2} = \sqrt{11}$ $\therefore \, m_3 < m_1 < m_4 < m_2$