A vector $2 \hat{i}+2\widehat{ j}$  rotated about its tail through an angle ${45}^{\circ }$ in clockwise direction. Then the new vector is

If a vector is rotated its magnitude does not change but direction changes .

$$\begin{gathered} Given vector is making {45}^0 with x axis. \\ After rotation of {45}^0 in clockwise direction, it will become parallel to x axis \\ without change in its magnitude. \\ So, new vector=2\sqrt{2} \hat{i} \end{gathered}$$