12th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-3

  • question_answer
    If the sum of two unit vectors is a unit vector, then the angle between them is equal to:

    A) \[\frac{\pi }{3}\]                        

    B) \[\frac{\pi }{6}\]             

    C) \[\frac{\pi }{2}\]                                    

    D) \[\frac{2\pi }{3}\]

    Correct Answer: D

    Solution :

    [d] Let \[\widehat{i}+\widehat{j}=\widehat{k}\] Squaring both sides, we have \[{{\left( \widehat{i} \right)}^{2}}+{{\left( \widehat{j} \right)}^{2}}+2\widehat{i}.j={{\left| \widehat{k} \right|}^{2}}\] \[\Rightarrow 1+1+2.\cos \theta =1\] \[\Rightarrow cos\theta =-\frac{1}{2}=-cos\frac{\pi }{3}\] \[=cos\theta =\left( \pi -\frac{\pi }{2} \right)\] \[=cos\theta =cos\frac{2\pi }{3}\] Hence, option [d] is correct.

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