Two vectors $a \hat{i}+b \hat{j}+\hat{k}$ and $2 \hat{i}-3 \hat{j}+4 \hat{k}$ are perpendicular to each other. When $3 \mathrm{a}+2 \mathrm{~b}=7$, the ratio of $a$ to $b$ is $\frac{x}{2}$. The value of $x$ is

The vector sum of two forces $\vec{A}$ and $\vec{B}$ is perpendicular to their vector difference. Hence forces $\vec{A}$ and $\vec{B}$ are

$$ \begin{aligned} & \text { If }|\vec{a}|=\sqrt{26},|\vec{b}|=7 \\ & |\vec{a} \times \vec{b}|=35 \text {, find } \vec{a} \cdot \vec{b} \end{aligned} $$