Question

use the figure to find the specified vector. find a - b. graph of vectors a and b on a coordinate plane 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 \(a\) has its initial point at \((0,0)\) and terminal point at \((3,7)\). So, \(a=\langle3 - 0,7 - 0
angle=\langle3,7
angle\).

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

Vector \(b\) has its initial point at \((0,0)\) and terminal point at \((- 8,4)\). So, \(b=\langle-8 - 0,4 - 0
angle=\langle-8,4
angle\).

Step3: Calculate \(a - b\)

Using the formula for vector subtraction \(\langle x_1,y_1
angle-\langle x_2,y_2
angle=\langle x_1 - x_2,y_1 - y_2
angle\).
Substitute \(x_1 = 3,y_1 = 7,x_2=-8,y_2 = 4\) into the formula:
\(a - b=\langle3-(-8),7 - 4
angle=\langle3 + 8,3
angle=\langle11,3
angle\).

Answer:

B. \(\langle11,3
angle\)