Question

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

Answer 1

First, write the vectors in an "easy" way,
\[\vec{A}+\vec{B}+\vec{C}=(-1.60,0)\] is what the problem states. Also in the graph, you see that, \[\vec{A}=(4,0)\\ \vec{C}=(0,-2)\] So you have,
\[(4,0)+\vec{B}+(0,-2)=(-1.60,0)\] From this point, you will find easily the solution.

To find the angle: as B will be of the form, B=(x,y), then angle can be obtained using trigonometric relations,
\[\theta=\arctan(y/x)\]