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

${m_3}\,\, < {m_1} < {m_2} < {m_4}$

${m_3}\,\, < {m_4} < {m_1} < {m_2}$

${m_3}\,\, < {m_4} < {m_2} < {m_1}$

JEE MATHEMATICS MCQ: ADDITION OF VECTORS

1 Easy

1 of 1

Application +4 | -1

{m_1},\,\,{m_2},\,\,{m_3}\;\mathrm{and\;}{m_4}

are respectively the magnitudes of the vectors

\overrightarrow {{\mathbf{a}_1}} = 2\widehat {\,\mathbf{\dot i}} - \widehat {\mathbf{\dot j}} + \mathbf{\hat k},\;\overrightarrow {\,{\mathbf{a}_2}} = 3\widehat {\mathbf{\dot i}} - 4\widehat {\mathbf{\dot j}} + 4\mathbf{\hat k},\;\overrightarrow {\,{\mathbf{a}_3}} = \widehat {\mathbf{\dot i}} + \widehat {\mathbf{\dot j}} - \mathbf{\hat k}\,\;\mathrm{and \;}\overrightarrow {{\mathbf{a}_4}} = \widehat { - \mathbf{\dot i}} + 3\widehat {\,\mathbf{\dot j}} + \mathbf{\hat k}

̂, then the correct order of

{m_1},\,\,{m_2},\,\,{m_3}\,\;\mathrm{and}\,\mathrm{\;}{m_4}

View answer and explanation

Correct option: A

{m_3}\,\, < {m_1} < {m_4} < {m_2}

Option A (

{m_3}\\ < {m_1} < {m_4} < {m_2}

) is correct because it accurately reflects the calculated magnitudes of the given vectors.