For the three vectors shown above in the figure, A⃗ +B⃗ +C⃗ =− 1.60 i^. What is vector B⃗ ? What is the magnitude of B⃗ ? How many degrees above the negative x-axis does B⃗ point?

Question

For the three vectors shown above in the figure, A⃗ +B⃗ +C⃗ =− 1.60 i^. What is vector B⃗ ? What is the magnitude of B⃗ ? How many degrees above the negative x-axis does B⃗  point?

mony01 · Answer

attachment

knowledge · Answer

I am trying to help you, but when you say vector A+B+C=-1.60 i^.  I don't get what you are trying to say

mony01 · Answer

vector A + vector B+ vector C=-1.60 i "hat"

knowledge · Answer

are you saying i as in the imaginary unit?

mony01 · Answer

no i hat meaning unit vectors that define the directions of the x and y axes

knowledge · Answer

oh okay

mony01 · Answer

@Knowledge are you able to help me?

knowledge · Answer

We know that the 
$$a=(4,0) $$ and $$c=(0,2)$$ and according to your question, a+b+c=(-1.6,0)  then that means that for b=(-5.6, -2).  This part is simple algebra as you can see.  The next question is the magnitude.  THe magnitude can be found using the square root of the sum of the squares of the compnents.  In this case square each component, add the result, then square root.  The direction can be found by using the fact that trigonometry.  The sine of the angle is the y component over the hypotenuse of the triangle formed when the x and the y components are legs.  So the legs will have a distance equal to the x and y values and you find the hypt and then use trig to find the direction.

mony01 · Answer

Can yuo explain the direction again? and for the magnitude i got sqrt(20), is that right?