$\overrightarrow A = 2\hat i + \hat j,\,B = 3\hat j - \hat k$ and $\overrightarrow C = 6\hat i - 2\hat k$.Value of $\overrightarrow A - 2\overrightarrow B + 3\overrightarrow C $ would be

  • A

    $20\hat i + 5\hat j + 4\hat k$

  • B

    $20\hat i - 5\hat j - 4\hat k$

  • C

    $4\hat i + 5\hat j + 20\hat k$

  • D

    $5\hat i + 4\hat j + 10\hat k$

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  • [AIIMS 2019]

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