Question

State parallelogram law of vectors addition . Find analytically the magnitude and direction of resultant vector , when (a) two vectors are parallel to each other (b) two vectors are perpendicular to each other.

Answer 1

$$\begin{gathered} Thisisamethodforfindingthesumofvectors.AccordingtothisLawiftwovectorsAandBarerepresentedbytwoadjacentsidesofParalle\log rampointinginoutward \\ direction,thenthediagonaldrawnthroughtheintersectionoftwovectorsrepresentsthevectorsumofAandB. \\ LetvectorAberepresentedassideOP,andvectorBasOQ. \\ MagnitudeofvectorAandBisgivenby \\ R=[A^2+B^2+2AB\cos \left(\theta \right){]}^{1/2} \\ where\theta istheangleAandB \\ (1)ifAandBareparalleli.e.\theta =0^0 \\ R=A+B \\ (2)IfAandBareperpendiculari.e.\theta ={90}^0 \\ R=[A^2+B^2{]}^{1/2} \end{gathered}$$