Questions: 2. Draw a diagram that shows vectors a) through d) below and then illustrate the resultant vector based on each movement. (3 marks) a. A car travels 4 km West b. The car turns and travels 2 km South c. The car turns again and travels 3 km West d. The car turns one final time and travels 6 km North.

Solution Steps

We start by representing each movement as a vector:

• Vector \( \mathbf{A} \): 4 km West, which can be written as \( \mathbf{A} = -4 \hat{i} \)
• Vector \( \mathbf{B} \): 2 km South, which can be written as \( \mathbf{B} = -2 \hat{j} \)
• Vector \( \mathbf{C} \): 3 km West, which can be written as \( \mathbf{C} = -3 \hat{i} \)
• Vector \( \mathbf{D} \): 6 km North, which can be written as \( \mathbf{D} = 6 \hat{j} \)

Next, we sum the vectors to find the resultant vector \( \mathbf{R} \): \[ \mathbf{R} = \mathbf{A} + \mathbf{B} + \mathbf{C} + \mathbf{D} \] \[ \mathbf{R} = (-4 \hat{i}) + (-2 \hat{j}) + (-3 \hat{i}) + (6 \hat{j}) \] \[ \mathbf{R} = (-4 - 3) \hat{i} + (-2 + 6) \hat{j} \] \[ \mathbf{R} = -7 \hat{i} + 4 \hat{j} \]

The resultant vector \( \mathbf{R} \) can be visualized as a vector starting from the origin and ending at the point \((-7, 4)\) in the Cartesian coordinate system.

Final Answer