Two particles travel along the space curves r1(t) = (t, t^2, t^3) and r2(t) = (1

Question

Two particles travel along the space curves r1(t) = (t, t^2, t^3) and r2(t) = (1 + 4t, 1 + 16t, 1 + 52t) Find the points at which their paths intersect. (If an answer does not exist, enter DNE.) a) (x,y,z) of smaller t value b) (x,y,z) of larger t value Find the points where the particles collide. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) c) t=...

Explanation / Answer

t = 1+4t => t = -1/3 t2 = 1+16t => t = 16.06 or t= -0.0622 t3 = 1+52t => t = 7.22 or -0.0192 or -7.201 Since the value of t is not common, therefore DNE. The particles will never collide.

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