Question

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 ?

Answer 1

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

Explanation:

Let's define Vector A and Vector B as `v_1` and `v_2` respectively.

`v_1=a_1i+b_1j`
`v_2=a_2i+b_2j`

This is what you get when you add `v_1` and `v_2`:
`v_1+v_2=(a_1+a_2)i+(b_1+b_2)j`

According to the given, `a_1+a_2=8.8` and `b_1+b_2=4.8`

This is what you get when you subtract `v_2` from `v_1`:
`v_1-v_2=(a_1-a_2)i+(b_1-b_2)j`

According to the given, `a_1-a_2=-5.6` and `b_1-b_2=6.8`

What we are looking for is the value of `a_1` and `b_2`. 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=8.8`
`a_1-a_2=-5.6`
`b_1+b_2=4.8`
`b_1-b_2=6.8`

For solving `a_1`:
`a_1+a_2=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)`