Resultant Of Vectors

The vectors $\overrightarrow{\mathrm{A}}$ $\mathrm{and}$ $\overrightarrow{\mathrm{B}}$ are such that: $\left|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}\right|=\left|\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}\right|$.
The angle between the two vectors is:
1.
2.
3.
4.

Three forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is:

1. $0.5$ $\mathrm{N}$

2. $1.5$ $\mathrm{N}$

3. $\frac{\sqrt{3}}{4}$ $\mathrm{N}$

4. $\sqrt{3}$ $\mathrm{N}$

Six vectors $\overrightarrow{\mathrm{a}}$ through $\overrightarrow{\mathrm{f}}$ have the magnitudes and directions indicated in the figure. Which of the following statements is true? 

1. $\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{f}}$

2. $\overrightarrow{\mathrm{d}}+\overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{f}}$

3. $\overrightarrow{\mathrm{d}}+\overrightarrow{\mathrm{e}}=\overrightarrow{\mathrm{f}}$

4. $\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{e}}=\overrightarrow{\mathrm{f}}$