\(\vec {v_1} + \vec {v_2} = (2\hat i - 3\hat j) + (-6\hat i + 5\hat j)\)
\(= (2\hat i - 6 \hat i) + (-3 \hat j + 5 \hat j)\)
\(= - 4 \hat i + 2 \hat j\)
\(\therefore |\vec {v_1} + \vec {v_2}| = \sqrt{(-4)^2 + 2^2}\)
\(= \sqrt {20}\)
\(= \sqrt {4 \times 5}\)
\(= 2 \sqrt 5\)
Comparing \(\vec {v_1} + \vec {v_2} \) with \(\vec R =R _x \hat i +R _y \hat j \)
\(\Rightarrow\) \( R_{x} = - 4\) and \(R_{y} = 2\)
Taking to be angle made by \(\vec R\) with X-axis,
\(\therefore \theta = \tan^{-1} \left(\frac{R_y}{R_x}\right)\)
\(= \tan^{-1} \left( \frac 2 {-4}\right)\)
\(= \tan^{-1} \left( \frac 1{-2}\right)\) with X-axis
