6. [In this question the unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are in a vertical plane, \(\mathbf { i }\) being horizontal and \(\mathbf { j }\) being vertically upwards.] At \(t = 0\) a particle \(P\) is projected from a fixed point \(O\) with velocity ( \(7 \mathbf { i } + 7 \sqrt { 3 } \mathbf { j }\) ) \(\mathrm { m } \mathrm { s } ^ { - 1 }\). The particle moves freely under gravity. The position vector of a point on the path of \(P\) is \(( x \mathbf { i } + y \mathbf { j } ) \mathrm { m }\) relative to \(O\).

1. Show that $$y = \sqrt { 3 } x - \frac { g } { 98 } x ^ { 2 }$$
2. Find the direction of motion of \(P\) when it passes through the point on the path where \(x = 20\) At time \(T\) seconds \(P\) passes through the point with position vector \(( 2 \lambda \mathbf { i } + \lambda \mathbf { j } ) \mathrm { m }\) where \(\lambda\) is a positive constant.
3. Find the value of \(T\).
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