Let a = i + j + k, b =2 i +4 j -5 k and c =x i +2 j +3 k, x ∈ R. If d is the unit vector in the direction of b + c such that a · d =1, then ( a × b )…

Let $\displaystyle \vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=2 \hat{i}+4 \hat{j}-5 \hat{k}$ and $\displaystyle \vec{c}=x \hat{i}+2 \hat{j}+3 \hat{k}, x \in \mathbb{R}$. If $\displaystyle \vec{d}$ is the unit vector in the direction of $\displaystyle \vec{b}+\vec{c}$ such that $\displaystyle \vec{a} \cdot \vec{d}=1$, then $\displaystyle (\vec{a} \times \vec{b}) \cdot \vec{c}$ is equal to