If $m_1, m_2, m_3$ and $m_4$ are respectively the magnitudes of the vectors $\overrightarrow{\mathbf{a}}_1=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \quad \overrightarrow{\mathbf{a}}_2=3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}$,…

Question

If $m_1, m_2, m_3$ and $m_4$ are respectively the magnitudes of the vectors $\overrightarrow{\mathbf{a}}_1=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \quad \overrightarrow{\mathbf{a}}_2=3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}$, $\overrightarrow{\mathbf{a}}_3=\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}} \quad$ and $\quad \overrightarrow{\mathbf{a}}_4=-\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}$, then the correct order of $m_1, m_2, m_3$ and $m_4$ is

Aicharya · Accepted Answer

Given, $\begin{aligned} & m_1=\left|\overrightarrow{\mathbf{a}}_1ight|=\sqrt{2^2+(-1)^2+(1)^2}=\sqrt{6} \ & m_2=\left|\overrightarrow{\mathbf{a}}_2ight|=\sqrt{3^2+(-4)^2+(-4)^2}=\sqrt{41} \ & m_3=\left|\overrightarrow{\mathbf{a}}_3ight|=\sqrt{1^2+1^2+(-1)^2}=\sqrt{3} \end{aligned}$ and $m_4=\left|\overrightarrow{\mathbf{a}}_4ight|=\sqrt{(-1)^2+(3)^2+(1)^2}=\sqrt{11}$ $	herefore \quad m_3 < m_1 < m_4 < m_2$

If $m_1, m_2, m_3$ and $m_4$ are respectively the magnitudes of the vectors $\overrightarrow{\mathbf{a}}_1=2…

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