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EAMCET Medical EAMCET Medical Solved Paper-2007

  • question_answer
    Given two vectors \[A\to =-\widehat{i}+2\widehat{j}-3\widehat{k}\] and \[B\to =4\widehat{i}+2\widehat{j}-6\widehat{k}.\]. The angle made by \[(A\to +B\to )\] with x-axis is

    A)  \[30{}^\circ \]                                  

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

    C) \[60{}^\circ \]                                   

    D) \[90{}^\circ \]

    Correct Answer: B

    Solution :

                     Given, \[\vec{A}=-\hat{i}+2\hat{j}-3\hat{k}\] \[\hat{B}=4\hat{i}-2\hat{j}+6\hat{k}\] Let angle made by \[(\vec{A}+\vec{B})\]with \[x-\]axis is \[\theta .\] \[\cos \theta =\frac{(\vec{A}+\vec{B}).\hat{i}}{|\vec{A}+\vec{B}|.|\hat{i}|}=\frac{(3\hat{i}+3\hat{k}).\hat{i}}{\sqrt{9+9}.1}\] \[=\frac{3}{3\sqrt{2}}=\frac{1}{\sqrt{2}}\]                 \[\therefore \]  \[\theta ={{45}^{o}}\]


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