Question

Find a vector equation and parametric equations for the line segment that joins P to Q. (D |-1+2-) 1 P(0, -1, 4) 4 -t.2 3 t. r(t) 4 vector equation X 7 4 t.2 3 1 - t. (x(t), y(t), z(t)) 4 X - parametric equations 2 If two objects travel through space along two different curves, it's often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) The curves might intersect, but we need to know whether the objects are in the same position at the same time. Suppose the trajectories of two particles are give by the vector functions r2(t) =(7t 12, t, 8t - 15) (t)(, 9t - 18, t2) for t2 0. Find the values of t at which the particles collide. (Enter your answers as comma-separated list. If an answer does not exist, enter DNE.) 4,6

Answer 1

Given P (0,-\,4) direton vedar P& = < t- Nector equalian ra negmant Pa (0,-1,4) = (a)) O1,4) +t Paramatne equation (t,-t, 4-1) x CES, y(), object travel long tha curver Tso 2, 3t-18, t3> andB() =<7t-12, 3, 8t-15 Nouo equating Coordinalos ,z t27t120alt-a) (tu)=o I-CoOrdinaa 2-Tt-12 t=3, 4 9-Coordinala st-18 t13 =0 -3) (t-6)= t- 3,6 ta8t-1s t-8t+s =d= t 3,S Z- Coordinata both curves meet at tha oint 9,g 9> At ta3, Tharetore barticle collides at t=3 t 3