# 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.

Eshan
askIITians Faculty 2095 Points
4 years ago
Dear student,

Since the resultant has only vertical component, the horizontal compoenents of both vectors must cancel each other. Hence$\dpi{80} A=B cos\theta$
Also from relation$\dpi{80} R^2=A^2+B^2-2ABcos\theta$and$\dpi{80} R=\dfrac{B}{\sqrt{2}}$,

$\dpi{80} \dfrac{B^2}{2}=A^2+B^2-2ABcos\theta$
$\dpi{80} \implies A^2+\dfrac{B^2}{2}=2ABcos\theta$
$\dpi{80} \implies B^2cos^2\theta+\dfrac{B^2}{2}=2B^2cos^2\theta$
$\dpi{80} \implies cos\theta=\dfrac{1}{\sqrt{2}}\implies \theta=45^{\circ}$