Question

use the figure to evaluate ( a + b ), ( a - b ), and ( - a ).
( a + b = langle 2,9
angle )
( a - b = langle square,square
angle )

Explanation:

Step1: Determine vectors a and b

From the graph, vector \( \mathbf{a} \) has components \( \langle -1, 5
angle \) (since it moves 1 unit left and 5 units up from the origin), and vector \( \mathbf{b} \) has components \( \langle 3, 4
angle \) (moves 3 units right and 4 units up from the origin).

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

To subtract vectors, we subtract their corresponding components. The formula for vector subtraction is \( \mathbf{a} - \mathbf{b} = \langle a_x - b_x, a_y - b_y
angle \).

Substituting the components:
\( a_x - b_x = -1 - 3 = -4 \)
\( a_y - b_y = 5 - 4 = 1 \)

So, \( \mathbf{a} - \mathbf{b} = \langle -4, 1
angle \).

Answer:

\( \langle -4, 1
angle \)