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  • Resultant of two vectors is of magnitude P. If <img alt="\

Resultant of two vectors \vec{A}\And \vec{B} is of magnitude P. If \vec{B} is reversed, the resultant is of magnitude Q. What is the value of {{P}^{2}}+{{Q}^{2}} ?

Option: 1

2({{A}^{2}}+{{B}^{2}})


Option: 2

2({{A}^{2}}-{{B}^{2}})


Option: 3

{{A}^{2}}-{{B}^{2}}


Option: 4

{{A}^{2}}+{{B}^{2}}


Answers (1)

best_answer

Let \theta be the angle between \vec{A}\And \vec{B}

Resultant of \vec{A}\And \vec{B} is ,

P=\sqrt{{{A}^{2}}+{{B}^{2}}+2AB\cos \theta }

When \vec{B} is reversed, then the angle between \vec{A}\And -\vec{B} is {{180}^{\circ }}-\theta

Resultant of \vec{A}\And -\vec{B} is,
Q=\sqrt{{{A}^{2}}+{{B}^{2}}+2AB\cos (180-\theta )} \\ Q=\sqrt{{{A}^{2}}+{{B}^{2}}-2AB\cos \theta } \\

Squaring and adding P and Q,

{{P}^{2}}+{{Q}^{2}}=2({{A}^{2}}+{{B}^{2}})

 

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Nehul

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