$\Rightarrow 13-1-4 \lambda=0 \Rightarrow \lambda=3$
$\Rightarrow \overrightarrow{ b }=\hat{ i }+\hat{ j }+3 \hat{ k } \Rightarrow \overrightarrow{ a } \times \overrightarrow{ b }=13 \hat{ i }-\hat{ j }-4 \hat{ k }$
$\Rightarrow(\overrightarrow{ a } \times \overrightarrow{ b }) \times \overrightarrow{ b }=(13 \hat{ i }-\hat{ j }-4 \hat{ k }) \times(\hat{ i }+\hat{ j }+3 \hat{ k })$
$\Rightarrow-21 \overrightarrow{ b }-11 \overrightarrow{ a }=\hat{ i }-43 \hat{ j }+14 \hat{ k }$
$\Rightarrow \overrightarrow{ a }=-2 \hat{ i }+2 \hat{ j }-7 \hat{ k }$
Now $(\overrightarrow{ b }-\overrightarrow{ a }) \cdot(\hat{ k }-\hat{ j })+(\overrightarrow{ b }+\overrightarrow{ a }) \cdot(\hat{ i }-\hat{ k })=14$
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