Question

use the figure to find the specified vector. find a - b. options: a. ⟨-11, -3⟩, b. ⟨11, 3⟩, c. ⟨-5, 3⟩, d. ⟨-5, 11⟩

Explanation:

Step1: Determine the components of vector \(a\)

From the figure, vector \(a\) goes from \((0,0)\) to \((3,7)\). So, \(a=\langle3 - 0,7 - 0
angle=\langle3,7
angle\).

Step2: Determine the components of vector \(b\)

Vector \(b\) goes from \((0,0)\) to \((- 8,4)\). So, \(b=\langle-8 - 0,4 - 0
angle=\langle-8,4
angle\).

Step3: Calculate \(a - b\)

Using the formula \(\langle x_1,y_1
angle-\langle x_2,y_2
angle=\langle x_1 - x_2,y_1 - y_2
angle\), we have \(a - b=\langle3-(-8),7 - 4
angle=\langle3 + 8,3
angle=\langle11,3
angle\).

Answer:

B. \(\langle11,3
angle\)