Travelling due north at a speed of 50 km/h , a motor car executes a...

Initial velocity of the car, $\vec{v}_1 = 50 \hat{j}$

Final velocity of the car after a 90^{}^{{}^{\circ}} left turn (towards west), $\vec{v}_2 = -50 \hat{i}$

Change in velocity, $\Delta \vec{v} = \vec{v}_2 - \vec{v}_1 = -50 \hat{i} - 50 \hat{j}$

Magnitude of change in velocity, $|\Delta \vec{v}| = \sqrt{(-50)^2 + (-50)^2} = 50\sqrt{2} \approx 70.7 \text{ km/h}$

The direction of $\Delta \vec{v}$ is along $- \hat{i} - \hat{j}$, which corresponds to the south-west direction.

Thus, the change in velocity is approximately $70 \text{ km/h}$ towards south-west.