Express a vector in Cartesian (component) form using the unit vectors 𝒊̂ and 𝒋̂.

Consider the vector **v** that has magnitude 10 units and makes an angle of 120° with the positive x-axis. (a) Determine the horizontal component of **v**. (1 mark) (b) Determine the vertical component of **v**. (1 mark) (c) Express **v** in Cartesian form using the unit vectors **i** and **j**. (1 mark)

A vector **v** has magnitude 10 and makes an angle of 150° with the positive x-axis, measured anticlockwise. Express **v** in the form $a\mathbf{\hat{i}} + b\mathbf{\hat{j}}$.

A drone is flying over flat terrain. At time t = 0 seconds, the drone is at point A with position vector **a** = 5**i** + 12**j**, where distances are measured in metres. At time t = 4 seconds, the drone is at point B with position vector **b** = 17**i** + 3**j**. (a) Express the displacement vector **AB** in Cartesian form using unit vectors **i** and **j**. (1 mark) (b) The drone travels at constant velocity. Find the velocity vector **v** of the drone in Cartesian form using unit vectors **i** and **j**. (1 mark) (c) At time t = 4 seconds, a second drone departs from point C with position vector **c** = 9**i** + 15**j** and travels with velocity vector **u** = 4**i** − 2**j** m/s. Express the position vector **r** of the second drone at time t seconds (for t ≥ 4) in Cartesian form using unit vectors **i** and **j**. (1 mark)

Which of the following expresses the vector **v** shown in the diagram in Cartesian form using unit vectors **i** and **j**?