# Which of the following pairs of displacements cannot be added to give a resultant displacement of 2m?1. 1m+1m2. 1m+2m3. 1m+3m4. 1m+4m

1 m and 4 m cannot be added to give result 2 m.
Applying vector addition for 1 m and 4 m
$R=\sqrt{{1}^{2}+{4}^{2}+2×1×4\mathrm{cos}\left(\theta \right)}\phantom{\rule{0ex}{0ex}}2=\sqrt{{1}^{2}+{4}^{2}+2×1×4\mathrm{cos}\left(\theta \right)}\phantom{\rule{0ex}{0ex}}squaring\phantom{\rule{0ex}{0ex}}4=17+8\mathrm{cos}\left(\theta \right)\phantom{\rule{0ex}{0ex}}\mathrm{cos}\left(\theta \right)=\frac{-13}{8}\phantom{\rule{0ex}{0ex}}$
There is no angle which can satisfy this equation.

For other option there is value of angle which gives result 2 m.

• 45
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