7 A particle is initially at the point \(A\), which has position vector \(13.6 \mathbf { i }\) metres, with respect to an origin \(O\). At the point \(A\), the particle has velocity \(( 6 \mathbf { i } + 2.4 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\), and in its subsequent motion, it has a constant acceleration of \(( - 0.8 \mathbf { i } + 0.1 \mathbf { j } ) \mathrm { ms } ^ { - 2 }\). The unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are directed east and north respectively.

1. Find an expression for the velocity of the particle \(t\) seconds after it leaves \(A\).
2. Find an expression for the position vector of the particle, with respect to the origin \(O\), \(t\) seconds after it leaves \(A\).
3. Find the distance of the particle from the origin \(O\) when it is travelling in a north-westerly direction.
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