Uppose r⃗ (t)=cos(πt)i+sin(πt)j+5tk represents the position of a particle on a helix, where z is the height of the particle. (a) what is t when the particle has height 15? t= 3 \displaystyle{3}3 (b) what is the velocity of the particle when its height is 15? v⃗ = < -pisin(3pi),picos(3pi),5> \displaystyle< -\pi{\sin{{\left({3}\pi\right)}}},\ pi{\cos{{\left({3}\pi\right)}}},{5} > < −πsin(3π),πcos(3π),5> (c) when the particle has height 15, it leaves the helix and moves along the tangent line at the constant velocity found in part (b). find a vector parametric equation for the position of the particle (in terms of the original parameter t) as it moves along this tangent line.