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3-1.Vectors
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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.........$N$ 
A$\frac{{\sqrt 3 }}{4}$
B$\sqrt 3$
C$0.5$
D$1.5$
Solution
Minimum additional force
$=| \mathrm{X}-$ component of given vector $|$
$=\left|1\left(\cos 60^{\circ}\right)+2 \cos 60^{\circ}-4 \cos 60^{\circ}\right|$
$=\left|\frac{1}{2}+2 \times \frac{1}{2}-4 \times \frac{1}{2}\right|=\left|-\frac{1}{2}\right|=\frac{1}{2}=0.5 \mathrm{N}$
$=| \mathrm{X}-$ component of given vector $|$
$=\left|1\left(\cos 60^{\circ}\right)+2 \cos 60^{\circ}-4 \cos 60^{\circ}\right|$
$=\left|\frac{1}{2}+2 \times \frac{1}{2}-4 \times \frac{1}{2}\right|=\left|-\frac{1}{2}\right|=\frac{1}{2}=0.5 \mathrm{N}$
Standard 11
Physics
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