- \hspace{0pt} [In this question, \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular unit vectors in a horizontal, \(x - y\) plane.]
A bead \(P\) of mass 0.08 kg is threaded on a smooth straight horizontal wire which lies along the line with equation \(y = 2 x - 1\). The unit of length on both axes is the metre. Initially the bead is at rest at the point \(( a , b )\). A force \(( 6 \mathbf { i } - 2 \mathbf { j } ) \mathrm { N }\) acts on \(P\) and moves it along the wire so that \(P\) passes through the point \(( 5,9 )\) with speed \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
Find the value of \(a\) and the value of \(b\).