Suppose the two particles travel along the space curves and . A collision will occur at the point of intersection P if both particles are at P at the same time. Find the point of collision.

Question

Suppose the two particles travel along the space curves  and  . A collision will occur at the point of intersection P if both particles are at P at the same time. Find the point of collision.

Quizplus · Accepted Answer

We can set the two space curves equal to each other to find the point of intersection: 
11eaa595_63b1_1108_a696_c5b490807f9f_TB4584_11_TB4584_11 = 11eaa595_63b1_3819_a696_e3bfbbf154ad_TB4584_11_TB4584_11 
This simplifies to: 
-201 + 17t = -55 + 7t 
Solving for t, we get: 
t = 32 
Now we can substitute t = 32 into either of the space curves to find the point of intersection: 
11eaa595_63b1_1108_a696_c5b490807f9f_TB4584_11_TB4584_11 (t = 32) = 11eaa595_63b1_863d_a696_6f041605f964_TB4584_11_TB4584_11 
So the point of collision is (32, -57, -10), which corresponds to choice D.

Suppose the Two Particles Travel Along the Space Curves