The Curve $\vec { r } ( t ) = a t \vec { i } + ( t + 4 ) \vec { j } + \left( b t ^ { 2 } + 6 \right) \vec { k }$

Short Answer

The curve $\vec { r } ( t ) = a t \vec { i } + ( t + 4 ) \vec { j } + \left( b t ^ { 2 } + 6 \right) \vec { k }$ passes through the point (-12, 1, 51).Find a and b.