The ratio of maximum and minimum magnitudes of the resultant of two vector $\vec a$ and $\vec b$ is $3 : 1$. Now $| \vec a |$  is equal to

  • A

    $| \vec b |$

  • B

    $2| \vec b |$

  • C

    $3| \vec b |$

  • D

    $4| \vec b |$

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  • [AIIMS 1998]

The position vectors of points $A, B, C$ and $D$ are $\vec A = 3\hat i + 4\hat j + 5\hat k,\,\vec B = 4\hat i + 5\hat j + 6\hat k,\,\vec C = 7\hat i + 9\hat j + 3\hat k$ and $\vec D = 4\hat i + 6\hat j$ then the displacement vectors $\overrightarrow {AB} $ and $\overrightarrow {CD} $ are