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  • the magniude and direction of the resultant of two vectors  and <img alt="\vec{B}" src="http:/

the magniude and direction of the resultant of two vectors \vec{A} and \vec{B} in terms of their magitudes and angle \theta between them is 

Option: 1

R=\sqrt{A^2+B^2-2AB\cos\theta},\: tan\alpha=\frac{B\sin\theta}{A+B\cos\theta}


Option: 2

R=\sqrt{A^2+B^2+2AB\cos\theta},\: tan\alpha=\frac{B\cos\theta}{A+B\sin\theta}


Option: 3

R=\sqrt{A^2+B^2-2AB\cos\theta},\: tan\alpha=\frac{A\sin\theta}{B+A\sin\theta}


Option: 4

R=\sqrt{A^{2}+B^{2}+2 A B \cos \theta}, \tan \alpha=\frac{B \sin \theta}{A+B \cos \theta}


Answers (1)

best_answer

In Parallelogram law of vector addition 

If two vector are represented by both magnitude and direction by two adjacent sides of a parallelogram taken from the same point then their resultant is also represented by both magnitude and direction taken from the same point but by diagonal of the parallelogram.

The figure given below represents the law of parallelogram vector Addition.

\vec{R} = \vec{A}+\vec{B}

  Using Pythagorean theorem in triangle MOP-

R^{^{2}} = (Bsin\Theta )^{2} + (A+Bcos\Theta )^{2}\\ \Rightarrow R=\sqrt{{A^{2}}+B^{2}+2ABcos\Theta } \\\\ \Rightarrow tan\alpha=\frac{Bsin\Theta }{A+Bcos\Theta }

Posted by

Gautam harsolia

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