$\overrightarrow{ b } \times \overrightarrow{ c }=\left|\begin{array}{ccc}\hat{ i } & \hat{ j } & \hat{ k } \\ 1 & -2 & -2 \\ -1 & 4 & 3\end{array}\right|=2 \hat{i}-\hat{ j }+2 \hat{ k }$
$\overrightarrow{ d }=\lambda(2 \hat{ i }-\hat{ j }+2 \hat{ k })$
$\vec{a} \cdot \vec{d}=18$
$\lambda=2$
So $\overrightarrow{ d }=2(2 \hat{ i }-\hat{ j }+2 \hat{ k })$
$\overrightarrow{ d } \times \overrightarrow{ a }=\left|\begin{array}{ccc}\hat{ i } & \hat{ j } & \hat{ k } \\ 4 & -2 & 4 \\ 2 & 3 & 4\end{array}\right|=-20 \hat{ i }-8 \hat{ j }+16 \hat{ k }$
$|\overrightarrow{ d } \times \overrightarrow{ a }|^2=720$
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વિધાન $1$:કોઇક $c\; \in R$ માટે, $f\left( c \right) = \frac{1}{3}$
વિધાન $2$:$0 < f\left( x \right) < \frac{1}{{2\sqrt 2 }}\;,\forall x\; \in R$