The correct answer to the question will be [tex]B^2=\ R^2\ -\ A^2[/tex].
EXPLANATION:
The two vectors are given as [tex]\vec A\ and\ \vec B[/tex].
As per the question, the two vectors intersect each other perpendicularly .
Hence, the angle between them is [tex][\theta]=\ 90^0[/tex]
The magnitude of resultant is given as R.
From parallelogram law of vector addition, the resultant R is calculated as -
[tex]R=\sqrt{A^2+B^2+2ABcos\theta}[/tex]
[tex]=\sqrt{A^2+B^2+2ABcos90}[/tex]
[tex]=\sqrt{A^2+B^2+2AB\times 0}[/tex]
[tex]=\sqrt{A^2+B^2}[/tex]
⇒ [tex]R^2=\ A^2+B^2[/tex]
⇒ [tex]B^2\ =\ R^2-A^2[/tex]
Hence, the correct relation for B will be [tex]B^2=R^2-A^2[/tex].
