Question

type the correct answer in each box.
the graph shows vectors a and b.
the resulting vector for b - a is < , >, and the resulting vector for 2a - b is < , >.

Explanation:

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

Vector \(\mathbf{a}\) starts at the origin \((0,0)\) and ends at \((3, -2)\), so \(\mathbf{a}=\langle 3, -2
angle\).
Vector \(\mathbf{b}\) starts at the origin \((0,0)\) and ends at \((-2, 5)\), so \(\mathbf{b}=\langle -2, 5
angle\).

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

Subtract corresponding components:
\(x\)-component: \(-2 - 3 = -5\)
\(y\)-component: \(5 - (-2) = 7\)
Thus, \(\mathbf{b} - \mathbf{a}=\langle -5, 7
angle\).

Step3: Calculate \(2\mathbf{a} - \mathbf{b}\)

First, find \(2\mathbf{a}\): \(2\mathbf{a}=2\langle 3, -2
angle=\langle 6, -4
angle\).
Then subtract \(\mathbf{b}\):
\(x\)-component: \(6 - (-2) = 8\)
\(y\)-component: \(-4 - 5 = -9\)
Thus, \(2\mathbf{a} - \mathbf{b}=\langle 8, -9
angle\).

Answer:

For \(\mathbf{b} - \mathbf{a}\): \(\langle \boldsymbol{-5}, \boldsymbol{7}
angle\)
For \(2\mathbf{a} - \mathbf{b}\): \(\langle \boldsymbol{8}, \boldsymbol{-9}
angle\)