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Two vectors having equal magnitudes A make an angle theta with each other.Find the magnitude and direction of the resultant.

anupriya , 9 Years ago

Grade 11

2 Answers

Neeti

Last Activity: 9 Years ago

The formula for resultant between two vectors is given by:

R=(A²+B²+2ABcos $\Theta$ )^½

^whereA and B are the magnitudes of the two vectors are $\Theta$ is the angle between them.

In this case magnitudes of the two vectors are same. Put the values as A and angle $\Theta$ you’ll get the resultant.

Angle(direction) is given by

tan $\Phi$ =Asin $\Theta$ /B+Acos $\Theta$

:)

Sandeepkumar

Last Activity: 7 Years ago

The magnitude of resultant will be B=√A^2+A^2+2AAcos theta =√2A^2(1+costheta)=√4A^2cos^2theta/2=2A cos theta/2The resultant will make an angle alpha with the first vector where tan alpha = Tan alpha =A sintheta / A+A cos theta =2A sintheta÷2costheta÷2/ 2A cos^2theta/2 =Tan theta/2

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