N1995 P1 Q12 [Modified]

Relative to an origin \(O\), points \(C\) and \(D\) have position vectors \(7\mathbf{i}+3\mathbf{j}+2\mathbf{k}\) and \(10\mathbf{i}+a\mathbf{j}+b\mathbf{k}\) respectively, where \(a\) and \(b\) are constants.

1. The straight line through \(C\) and \(D\) has equation \(\mathbf{r}=\left( \begin{matrix} 7 \\ 3 \\ 2 \\ \end{matrix} \right)+t\left( \begin{matrix} 1 \\ 3 \\ 0 \\ \end{matrix} \right)\), \(t\in \mathbb{R}\). Find the values of \(a\) and \(b\).
2. Calculate the acute angle between the straight line though \(C\) and \(D\) and the \(y\)-axis, giving your correct answer to the nearest \({{0.1}^{\circ }}\).
3. Find the position vector of the point \(Q\) on the line \(CD\) such that the angle between \(\overrightarrow{OQ}\) and \(\overrightarrow{OC}\) is equal to the angle between \(\overrightarrow{OQ}\) and \(\overrightarrow{OD}\) .