If Vector B is added to Vector A , the result is 8.8 i +4.8 j. If Vector B is subtracted from Vector A, the result is -5.6 i + 6.8 j . What is the magnitude of vector A ?

1 Answer
Sep 25, 2015

The magnitude of Vector A is 1.6i+5.8j1.6i+5.8j.

Explanation:

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)jv1v2=(a1a2)i+(b1b2)j

According to the given, a_1-a_2=-5.6a1a2=5.6 and b_1-b_2=6.8b1b2=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=-5.6a1a2=5.6
b_1+b_2=4.8b1+b2=4.8
b_1-b_2=6.8b1b2=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)