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WB JEE Medical WB JEE Medical Solved Paper-2009

  • question_answer
    \[\overset{\to }{\mathop{\text{A}}}\,\text{ and }\overset{\to }{\mathop{\text{B}}}\,\] are two vectors given by \[\overset{\to }{\mathop{\text{A}}}\,\text{=2}\overset{\hat{\ }}{\mathop{\text{i}}}\,\text{+3}\overset{\hat{\ }}{\mathop{\text{j}}}\,\text{ and }\overset{\to }{\mathop{\text{B}}}\,=\,\overset{\hat{\ }}{\mathop{\text{i}}}\,\text{+}\overset{\hat{\ }}{\mathop{\text{j}}}\,\] The magnitude of the component of \[\overset{\to }{\mathop{\text{A}}}\,\] along \[\overset{\to }{\mathop{\text{B}}}\,\] is

    A)  \[\frac{5}{\sqrt{2}}\]                                    

    B)  \[\frac{3}{\sqrt{2}}\]

    C)  \[\frac{7}{\sqrt{2}}\]                                    

    D)  \[\frac{1}{\sqrt{2}}\]

    Correct Answer: A

    Solution :

                     Magnitude of component of \[\text{\vec{A}}\]along \[\text{\vec{B}}\]\[\text{\vec{B}=}\frac{\vec{A}.\vec{B}}{|\vec{B}|}\] \[=\frac{(2i+3\hat{j}).(\hat{i}+\hat{j})}{\sqrt{2}}\] \[=\frac{2+3}{\sqrt{2}}=\frac{5}{\sqrt{2}}\]


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