Question

use the figure to evaluate ( mathbf{a}+mathbf{b}, mathbf{a}-mathbf{b} ), and ( -mathbf{a} ).
( mathbf{a}+mathbf{b}=langlesquare, square
angle )

Explanation:

Step1: Determine vectors a and b

From the graph, vector \( \mathbf{a} \) has initial point at the origin \((0,0)\) and terminal point at \((-1, 3)\), so \( \mathbf{a} = \langle -1, 3
angle \). Vector \( \mathbf{b} \) has initial point at the origin \((0,0)\) and terminal point at \((2, 4)\), so \( \mathbf{b} = \langle 2, 4
angle \).

Step2: Add vectors a and b

To add vectors, we add their corresponding components. So \( \mathbf{a} + \mathbf{b} = \langle -1 + 2, 3 + 4
angle \).

Step3: Calculate the sum

Calculating the components: \(-1 + 2 = 1\) and \(3 + 4 = 7\). So \( \mathbf{a} + \mathbf{b} = \langle 1, 7
angle \).

Answer:

\(\langle 1, 7
angle\)