Sketch the vector diagram.

Step 1: Sketch the vector diagram. To illustrate the given information, we draw a coordinate system with North pointing upwards, South downwards, East to the right, and West to the left. All vectors originate from the central point (origin). Vector 1 (V_1 = 3 ms^-1 N45W): Draw an arrow from the origin into the second quadrant, exactly halfway between the North (positive y-axis) and West (negative x-axis) directions. This vector makes an angle of 45^ with the North axis towards the West, or 135^ counter-clockwise from the positive East (x-axis). Vector 2 (V_2 = 12 ms^-1 W): Draw an arrow from the origin directly along the negative x-axis (West direction). Vector 3 (V_3 = 5 ms^-1 S): Draw an arrow from the origin directly along the negative y-axis (South direction). The resultant vector would be drawn from the origin to the final position if these vectors were added head-to-tail. Step 2: Resolve each vector into its horizontal (x) and vertical (y) components. Let the positive x-axis be East and the positive y-axis be North. For V_1 = 3 ms^-1 N45W: The angle from the positive x-axis is 90^ + 45^ = 135^. V_1x = 3 (135^) = 3 (-sqrt(2)2) = -1.5sqrt(2) ms^-1 V_1y = 3 (135^) = 3 (sqrt(2)2) = 1.5sqrt(2) ms^-1 For V_2 = 12 ms^-1 W: The angle from the positive x-axis is 180^. V_2x = 12 (180^) = 12(-1) = -12 ms^-1 V_2y = 12 (180^) = 12(0) = 0 ms^-1 For V_3 = 5 ms^-1 S: The angle from the positive x-axis is 270^. V_3x = 5 (270^) = 5(0) = 0 ms^-1 V_3y = 5 (270^) = 5(-1) = -5 ms^-1 Step 3: Sum the x-components and y-components to find the resultant components. R_x = V_1x + V_2x + V_3x = -1.5sqrt(2) - 12 + 0 = -12 - 1.5sqrt(2) ms^-1 R_y = V_1y + V_2y + V_3y = 1.5sqrt(2) + 0 - 5 = -5 + 1.5sqrt(2) ms^-1 Using sqrt(2) ≈ 1.414: R_x ≈ -12 - 1.5(1.414) = -12 - 2.121 = -14.121 ms^-1 R_y ≈ -5 + 1.5(1.414) = -5 + 2.121 = -2.879 ms^-1 Step 4: Calculate the magnitude of the resultant vector. The magnitude R is given by: R = sqrt(R_x^2 + R_y^2) R = sqrt((-14.121)^2 + (-2.879)^2) R = sqrt(199.39 + 8.288) R = sqrt(207.678) R ≈ 14.41 ms^-1 Step 5: Calculate the direction of the resultant vector. Since both R_x and R_y are negative, the resultant vector lies in the third quadrant (South-West). Let be the angle the resultant makes with the negative x-axis (West). = |(R_y)/(R_x)| = |(-2.879)/(-14.121)| = (2.879)/(14.121) ≈ 0.20387 = (0.20387) ≈ 11.53^ The direction can be stated as 11.53^ South of West (W11.53S). The resultant of the three vectors is 14.41 ms^-1 at 11.53^ South of West. Drop the next question.