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Let Two non-collinear vectors `vec a` and `vec b` inclined at angle of `[2pi]/3` be such that `|vec a|=3` and `|vec b|=4`.A point P moves so that at any time t the position vector `vec [OP]` (where O is the origin) is given as `vec [OP]=(e^t+e^-t)vec a +(e^t-e^-t)vec b`.If the least distance of P from the origin is `sqrt2sqrt[sqrtp-q]` where `p,q in N`,then find the value of p+q.

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