If $\vec{a} = 2\hat{i} - 3\hat{j} + 4\hat{k}$ and $\vec{b} = \hat{i} + 2\hat{j} - \hat{k}$,then $\vec{a} + \vec{b} = \dots$

  • A
    $3\hat{i} - \hat{j} + 3\hat{k}$
  • B
    $3\hat{i} + \hat{j} + 3\hat{k}$
  • C
    $\hat{i} - \hat{j} - 3\hat{k}$
  • D
    $2\hat{i} + \hat{j} + \hat{k}$

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If $\bar{a} = \hat{i} + \hat{j} + \hat{k}$,$\bar{b} = 4\hat{i} - 2\hat{j} + 3\hat{k}$,and $\bar{c} = \hat{i} - 2\hat{j} + \hat{k}$,then the vector of magnitude $6$ units,which is parallel to the vector $2\bar{a} - \bar{b} + 3\bar{c}$,is:

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