- \hspace{0pt} [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal unit vectors.]
A small bead of mass 0.5 kg is threaded on a smooth horizontal wire. The bead is initially at rest at the point with position vector \(( \mathbf { i } - 6 \mathbf { j } ) \mathrm { m }\). A constant horizontal force \(\mathbf { P } \mathrm { N }\) then acts on the bead causing it to move along the wire. The bead passes through the point with position vector ( \(7 \mathbf { i } - 14 \mathbf { j }\) ) m with speed \(2 \sqrt { 7 } \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
Given that \(\mathbf { P }\) is parallel to ( \(6 \mathbf { i } + \mathbf { j }\) ), find \(\mathbf { P }\).
(6)