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The real part of complex number z= 2a+i\left ( 7-a \right ) when z becomes purely real will be \left ( a\: \epsilon\: R \right )

Let $\underset{u}{\rightarrow}$ be a vector coplanar with the vectors $\underset{a}{\rightarrow}$ $= 2\hat{i}+3\hat{j}-\hat{k}$ and $\underset{b}{\rightarrow}$ $= \hat{j}+\hat{k}$ . If $\underset{u}{\rightarrow}$ is perpendicular to $\underset{a}{\rightarrow}$ and $\underset{u}{\rightarrow}$ • $\underset{b}{\rightarrow}$ = 24, then $\left | \vec{u} \right |^{2}$ is equal to :

Option 1) 84

Option 2) 336

Option 3) 315

Option 4) 256

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