Question

use the figure to evaluate ( a + b ), ( a - b ), and ( - a ).

( a + b = langle square, square
angle )

Explanation:

Step1: Determine vectors \(\mathbf{a}\) and \(\mathbf{b}\)

From the grid, vector \(\mathbf{a}\) has a horizontal component of \(-1\) (since it moves 1 unit left from the origin) and a vertical component of \(4\) (moves 4 units up). So \(\mathbf{a} = \langle -1, 4
angle\).
Vector \(\mathbf{b}\) has a horizontal component of \(3\) (moves 3 units right) and a vertical component of \(4\) (moves 4 units up). So \(\mathbf{b} = \langle 3, 4
angle\).

Step2: Calculate \(\mathbf{a} + \mathbf{b}\)

To add vectors, add their corresponding components:
\(\mathbf{a} + \mathbf{b} = \langle -1 + 3, 4 + 4
angle\)
Simplify the components:
\(-1 + 3 = 2\) and \(4 + 4 = 8\).

Answer:

\(\mathbf{a + b} = \langle 2, 8
angle\)