JEE Main & Advanced Physics Vectors Question Bank Addition and Subtraction of Vectors

  • question_answer
    Two forces \[{{\vec{F}}_{1}}=5\hat{i}+10\hat{j}-20\hat{k}\]and \[{{\vec{F}}_{2}}=10\hat{i}-5\hat{j}-15\hat{k}\] act on a single point. The angle between \[{{\vec{F}}_{1}}\]and \[{{\vec{F}}_{2}}\] is nearly                                      [AMU 1995]

    A)                 \[\text{3}0{}^\circ \]      

    B)                 \[\text{45}{}^\circ \]

    C)                 \[\text{6}0{}^\circ \]      

    D)                 \[\text{9}0{}^\circ \]

    Correct Answer: B

    Solution :

                        \[\cos \theta =\frac{\overrightarrow{{{F}_{1}}}.\overrightarrow{{{F}_{2}}}}{|{{F}_{1}}||{{F}_{2}}|}\]                                 \[=\frac{(5\hat{i}+10\hat{j}-20\hat{k}).(10\hat{i}-5\hat{j}-15\hat{k})}{\sqrt{25+100+400}\sqrt{100+25+225}}\]\[=\frac{50-50+300}{\sqrt{525}\sqrt{350}}\]                                 Þ \[\cos \theta =\frac{1}{\sqrt{2}}\]\[\therefore \] \[\theta =45{}^\circ \]


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