3. (a) Two particles travel along the curves ř1 (t) = (t² + 3, t+1,6/t), ř2(u) = (4u, 2u – 2, u² – 7). Find the points were the particles collide and the points where the paths intersect. At a point of intersection that is not a collision point find the angle between the tangent lines. (b) Find parametric equations for the line tangent to the helix r(t) = (/2 cos t)ĩ+ (/2sin t)j + tk at the point where t = }. At which points on the helix are the tangent lines perpendicular to the line x = y, z = 0?

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