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CMC Medical CMC-Medical Ludhiana Solved Paper-2007

  • question_answer
    If \[\overrightarrow{a}=2\widehat{i}-3\widehat{j}+\widehat{k}\] and  \[\overrightarrow{b}=3\widehat{i}-3\widehat{j}+2\widehat{k},\] the cosine of angle \[\theta \] between them is equal to

    A)  \[\frac{5}{14}\]

    B)  \[\frac{1}{7}\]

    C)  \[\frac{3}{14}\]                               

    D)  \[\frac{1}{14}\]

    Correct Answer: D

    Solution :

                    \[\overset{\to }{\mathop{a}}\,\,\cdot \overset{\to }{\mathop{b}}\,=ab\cos \theta \] \[\therefore \]\[(2\hat{i}-3\hat{j}+\hat{k})\cdot (3\hat{i}+\hat{j}-2\hat{k})=ab\cos \theta \] \[\Rightarrow \]               \[6-3-2=\sqrt{(4+9+1)\,(9+1+4)}\cos \theta \] \[\Rightarrow \]               \[1=\sqrt{14\times 14}\cos \theta \] \[\Rightarrow \]               \[1=14\cos \theta \] \[\Rightarrow \]               \[\cos \theta =\frac{1}{14}\]


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