Ratios of Distances between Centroid, Circumcenter, Incenter and Orthocenter of Triangle

Q.

If $\sin \left(\mathrm{x}\right)=0.7$, how do you list all possible values of $x.\mathrm{if}-180<x<180$?

Q. Given orthocentre $\overline{H}$ and circumcentre $\overline{C}$ for a triangle as $2\hat{i}+3\hat{j}and4\hat{i}+5\hat{k}$.Then the centroid of triangle can be given by,

1. $\frac{10\hat{i}-13\hat{j}}{3}$
2. $\frac{-10\hat{i}+13\hat{j}}{3}$
3. $\frac{10\hat{i}+13\hat{j}}{3}$
4. $\frac{-10\hat{i}-13\hat{j}}{3}$

Q. Given position vectors $\overline{a},\overline{b},\overline{c}$ of points A, B, C for a triangle. The centroid can be given by

1. $\frac{\overline{a}+\overline{b}+\overline{c}}{3}$
2. $\frac{2}{3}(\overline{a}+\overline{b}+\overline{c})$
3. $\overline{a}+\overline{b}+\overline{c}$
4. $\frac{(\overline{a}.\overline{b})\times \overline{c}}{3}$