Vector Operations: Finding a - b Using a Graph

Q35. Find the vector a - b using the given graph.

Background

Topic: Vector Operations

This question tests your understanding of vector subtraction using graphical representations. You are asked to find the vector difference a - b, which means subtracting vector b from vector a.

Key Terms and Formulas:

• Vector subtraction: If vectors a and b are given as and , then a - b = .

• Component form: Vectors are often written as where x is the horizontal component and y is the vertical component.

Step-by-Step Guidance

1. Identify the coordinates of vector a and vector b from the graph. Vector a starts at the origin and ends at (3, 7). Vector b starts at the origin and ends at (-8, 3).

2. Write the component forms: a = <3, 7>, b = <-8, 3>.

3. Set up the subtraction: a - b = <3, 7> - <-8, 3>.

4. Subtract the corresponding components: For the x-component, subtract -8 from 3. For the y-component, subtract 3 from 7.

Try solving on your own before revealing the answer!

Final Answer: <11, 4>

$a - b = <3 - (-8), 7 - 3> = <11, 4>$

Subtracting the components gives the vector <11, 4>, which represents the difference between a and b.