A) \[\left| Z \right|=\left| X\,-Y \right|\]
B) \[\left| Z \right|<\left| X\,-Y \right|\]
C) \[\left| Z \right|>\left| X\,\,-\,\,Y \right|\]
D) \[\left| Z \right|=\left| X+Y \right|\]
Correct Answer: B
Solution :
If \[\left| Z \right|\] is resultant between X and Y, then \[\left| Z \right| = \sqrt{{{X}^{2}}+{{Y}^{2}}+ 2XYcos 120{}^\circ }\] \[=\,\,\,\sqrt{{{X}^{2}}+{{Y}^{2}}-XY}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ as\,\,cos\,\,120{}^\circ \,\,=\,\,\frac{-1}{2} \right]\] Similarly, \[\left| \operatorname{X} - Y \right| \,=\,\,\sqrt{{{X}^{2}}+{{Y}^{2}}-2XY\,\,cos\,\,120{}^\circ }\] \[=\,\,\,\,\sqrt{{{X}^{2}}+{{Y}^{2}}+XY}\]\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\left| X\,\,-\,\,Y \right|>\,\,\left| Z \right|\]
You need to login to perform this action.
You will be redirected in
3 sec
