If vectors $P, Q$ and $R$ have magnitude $5, 12$ and $13 $ units and $\overrightarrow P + \overrightarrow Q = \overrightarrow R ,$ the angle between $Q$ and $R$ is

  • A

    ${\cos ^{ - 1}}\frac{5}{{12}}$

  • B

    ${\cos ^{ - 1}}\frac{5}{{13}}$

  • C

    ${\cos ^{ - 1}}\frac{{12}}{{13}}$

  • D

    ${\cos ^{ - 1}}\frac{7}{{13}}$

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  • [AIEEE 2002]