Question

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

Explanation:

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

From the figure, vector \(\mathbf{a}\) has components \(\langle 0, 5
angle\) (since it's along the y - axis, x - component is 0 and y - component is 5). Vector \(\mathbf{b}\) has components \(\langle 2, 4
angle\) (by counting the grid units: from the origin, it moves 2 units in x - direction and 4 units in y - direction).

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

The formula for subtracting two vectors \(\mathbf{u}=\langle u_1,u_2
angle\) and \(\mathbf{v}=\langle v_1,v_2
angle\) is \(\mathbf{u}-\mathbf{v}=\langle u_1 - v_1,u_2 - v_2
angle\).
For \(\mathbf{a}=\langle 0,5
angle\) and \(\mathbf{b}=\langle 2,4
angle\), we have:
\(a_1 - b_1=0 - 2=- 2\)
\(a_2 - b_2=5 - 4 = 1\)
So \(\mathbf{a}-\mathbf{b}=\langle-2,1
angle\)

Answer:

\(\langle - 2,1
angle\)