If a particle moves from point $P (2,3,5)$ to point $Q (3,4,5)$. Its displacement vector be

  • A

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

  • B

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

  • C

    $\hat i + \hat j$

  • D

    $2\hat i + 4\hat j + 6\hat k$

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  • [JEE MAIN 2022]

Establish the following vector inequalities geometrically or otherwise:

$(a)$ $\quad| a + b | \leq| a |+| b |$

$(b)$ $\quad| a + b | \geq| a |-| b |$

$(c)$ $\quad| a - b | \leq| a |+| b |$

$(d)$ $\quad| a - b | \geq| a |-| b |$

When does the equality sign above apply?