JEE Main & Advanced Physics Vectors Question Bank Fundamentals of Vectors

  • question_answer With respect to a rectangular cartesian coordinate system, three vectors are expressed as            \[\vec{a}=4\hat{i}-\hat{j}\], \[\vec{b}=-3\hat{i}+2\hat{j}\] and      \[\vec{c}=-\hat{k}\]            where \[\hat{i},\,\hat{j},\,\hat{k}\]are unit vectors, along the X, Y and Z-axis respectively. The unit vectors \[\hat{r}\]along the direction of sum of these vector is [Kerala CET (Engg.) 2003]

    A)            \[\hat{r}=\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}-\hat{k})\]         

    B)            \[\hat{r}=\frac{1}{\sqrt{2}}(\hat{i}+\hat{j}-\hat{k})\]

    C)            \[\hat{r}=\frac{1}{3}(\hat{i}-\hat{j}+\hat{k})\]        

    D)            \[\hat{r}=\frac{1}{\sqrt{2}}(\hat{i}+\hat{j}+\hat{k})\]

    Correct Answer: A

    Solution :

                 \[\vec{r}=\vec{a}+\vec{b}+\vec{c}\]\[=4\hat{i}-\hat{j}-3\hat{i}+2\hat{j}-\hat{k}\]\[=\hat{i}+\hat{j}-\hat{k}\]                    \[\hat{r}=\frac{{\vec{r}}}{|r|}=\frac{\hat{i}+\hat{j}-\hat{k}}{\sqrt{{{1}^{2}}+{{1}^{2}}+{{(-1)}^{2}}}}=\frac{\hat{i}+\hat{j}-\hat{k}}{\sqrt{3}}\]


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