Draw a vector N to represent a wind blowing north at 55 km per hour for one hour and a vector M representing a car travelling west that has gone 45 km.

Question 9: Step 1: Identify the operation. The question asks to "multiply" two 2D vectors. In vector algebra, the standard multiplication that results in a scalar is the dot product. Step 2: Define the vectors. Let v = 5 \\ -4 and u = -8 \\ 7 . Step 3: Calculate the dot product. The dot product of two vectors a = a_x \\ a_y and b = b_x \\ b_y is given by the formula a · b = a_x b_x + a_y b_y. v · u = (5)(-8) + (-4)(7) v · u = -40 - 28 v · u = -68 The result of multiplying vector v by vector u (dot product) is: -68 Question 10: Step 1: Determine the magnitudes and directions of the vectors. • Vector N (wind): The wind blows north at 55 km per hour for one hour, so its magnitude is 55 km. Its direction is North. • Vector M (car): The car travels west and has gone 45 km, so its magnitude is 45 km. Its direction is West. Step 2: Choose a suitable scale for the grid. The grid is 8x8 squares. A convenient scale that allows both vectors to be represented clearly within the grid is to let each square represent 10 km. • For Vector N: 55 km ÷ 10 km/square = 5.5 squares. • For Vector M: 45 km ÷ 10 km/square = 4.5 squares. Step 3: Describe how to draw each vector on the grid. Assume the bottom-left corner of the grid is the origin (0,0) and the top-right is (8,8). • Vector N (Wind): Start at a point, for example, the center of the bottom edge of the grid, which can be represented as (4,0). Draw an arrow pointing vertically upwards (North) from this starting point. The length of the arrow should be 5.5 squares. The arrow would end at (4, 5.5). • Vector M (Car): Start at a different point, for example, the center of the right edge of the grid, which can be represented as (8,4). Draw an arrow pointing horizontally leftwards (West) from this starting point. The length of the arrow should be 4.5 squares. The arrow would end at (3.5, 4). That's 2 down. 3 left today — send the next one.