JEE Main & Advanced Mathematics Vector Algebra Question Bank Scaler or Dot product of two vectors and its application

  • question_answer
    If the sum of two unit vectors is a unit vector, then the magnitude of their difference is [Kurukshetra CEE 1996; RPET 1996]

    A)             \[\sqrt{2}\]

    B)             \[\sqrt{3}\]

    C)             \[\frac{1}{\sqrt{3}}\]

    D)             1

    Correct Answer: B

    Solution :

               Let \[|\mathbf{a}|=1\] and \[|\mathbf{b}|=1\]            Also \[|\mathbf{a}+\mathbf{b}{{|}^{2}}={{1}^{2}}\Rightarrow 1+1+2\cos \theta =1\]\[\Rightarrow \theta =120{}^\circ \]                 \[\therefore \,\,\,|\mathbf{a}-\mathbf{b}{{|}^{2}}=1+1-2\cos \theta =3\]\[\Rightarrow \,|\mathbf{a}-\mathbf{b}|\,=\sqrt{3}.\]


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