A particle moves along a curve $y=x^2$ with constant speed of $10 \mathrm{m} {\mathrm{s}}^{–1}.$ When the particle is at origin, then the radius of curvature of path is $n \mathrm{m}.$ The value of $n$ is _____.

An object moves at constant speed along a circular path in a horizontal $xy$ plane, with center at origin. When the object is at $x=-2 \mathrm{m},$ its velocity is $-4\hat{j} \mathrm{m} {\mathrm{s}}^{-1}.$ Its acceleration when it is at $y=2 \mathrm{m}$ is

Three vectors $P, Q$ and $R$ are shown in the figure. Let $S$ be any point on the vector $R.$ The distance between the points $P$ and $S$ is $b\left[R\right].$ The general relation among vectors $P, Q$ and $S$ is,