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In vector diagram show n in figure where R bar is the resultant of A bar and B bar.If R=B/√2,then find the value of theta.

In vector diagram show n in figure where R bar is the resultant of A bar and B bar.If R=B/√2,then find the value of theta.

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Grade:12th pass

1 Answers

Eshan
askIITians Faculty 2095 Points
3 years ago
Dear student,

Since the resultant has only vertical component, the horizontal compoenents of both vectors must cancel each other. HenceA=B cos\theta
Also from relationR^2=A^2+B^2-2ABcos\thetaandR=\dfrac{B}{\sqrt{2}},

\dfrac{B^2}{2}=A^2+B^2-2ABcos\theta
\implies A^2+\dfrac{B^2}{2}=2ABcos\theta
\implies B^2cos^2\theta+\dfrac{B^2}{2}=2B^2cos^2\theta
\implies cos\theta=\dfrac{1}{\sqrt{2}}\implies \theta=45^{\circ}

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