Questions: Use a piece of scratch paper to make a sketch to show the addition of vectors D+G+B. Measuring in terms of number of boxes on the graph paper, what is the size of the RESULTANT? (How many boxes long?)

Use a piece of scratch paper to make a sketch to show the addition of vectors D+G+B. Measuring in terms of number of boxes on the graph paper, what is the size of the RESULTANT? (How many boxes long?)

Transcript text: Use a piece of scratch paper to make a sketch to show the addition of vectors $D+G+B$. Measuring in terms of number of boxes on the graph paper, what is the size of the RESULTANT? (How many boxes long?)

Solution

Solution Steps

Step 1: Represent vectors as components

Vector D is 3 units down and 2 units right, represented as (2, -3). Vector G is 2 units up and 3 units right, represented as (3, 2). Vector B is 1 unit up and 2 units left, represented as (-2, 1).

Step 2: Add the vectors

Adding the vectors component-wise: (2, -3) + (3, 2) + (-2, 1) = (2 + 3 - 2, -3 + 2 + 1) = (3, 0)

Step 3: Find the magnitude of the resultant vector

The resultant vector is (3, 0). Its magnitude is the square root of the sum of the squares of its components: sqrt(3^2 + 0^2) = sqrt(9) = 3.