Let's define Vector A and Vector B as v_1v1 and v_2v2 respectively.
v_1=a_1i+b_1jv1=a1i+b1j
v_2=a_2i+b_2jv2=a2i+b2j
This is what you get when you add v_1v1 and v_2v2:
v_1+v_2=(a_1+a_2)i+(b_1+b_2)jv1+v2=(a1+a2)i+(b1+b2)j
According to the given, a_1+a_2=8.8a1+a2=8.8 and b_1+b_2=4.8b1+b2=4.8
This is what you get when you subtract v_2v2 from v_1v1:
v_1-v_2=(a_1-a_2)i+(b_1-b_2)jv1−v2=(a1−a2)i+(b1−b2)j
According to the given, a_1-a_2=-5.6a1−a2=−5.6 and b_1-b_2=6.8b1−b2=6.8
What we are looking for is the value of a_1a1 and b_2b2. We will find these values by creating systems of equations and applying the elimination method. We will use the following equations:
a_1+a_2=8.8a1+a2=8.8
a_1-a_2=-5.6a1−a2=−5.6
b_1+b_2=4.8b1+b2=4.8
b_1-b_2=6.8b1−b2=6.8
For solving a_1a1:
a_1+a_2=8.8a1+a2=8.8
ul(a_1-a_2=-5.6)
2a_1=3.2
color(blue)(a_1=1.6)
For solving b_1:
b_1+b_2=4.8
ul(b_1-b_2=6.8)
2b_1=11.6
color(red)(b_1=5.8)
Now that we have the values of a_1 and b_1, let's plug in those values into our equation for v_1.
v_1=color(blue)(a_1)i+color(red)(b_1)j
v_1=color(blue)((1.6))i+color(red)((5.8))j
color(magenta)(v_1=1.6i+5.8j)