please show all the steps as clearly as possible. im having a really hard time w
ID: 2848214 • Letter: P
Question
please show all the steps as clearly as possible. im having a really hard time with this. please help.
you are in outer space
DEDICATED to GRAVITY: You are in outer space in a spaceship that has run out of fuel, drifting in space in the direction of from location (2, -3, 1) and needing to be reequipped with power and supplies. The closest supply station is located at (10, 5, 10) and it sends out a supply vessel perpendicular to your projected line of flight, Try to sketch the situation for partial credit. What will this minimal distance to your line of flight? What direction did the sheet take? In terms of your flight parameter, t = time (say in hours), when does this closest approach occur? What is this interception point?Explanation / Answer
(a)
let A(2-t, -3+t, 1+2t) be the interception, B =(10,5,10), C = (2,-3,1)
=>AB is perpendicular to line of motion (-1,1,2)
=>
(-t-8, -8+t,2t-9)*(-1,1,2) = 0
=>
t+8 + t-8 +2(2t-9) = 0
=>
6t = 18
=>
t = 3
=>
A = (-1,0,7)
(a)
minimal distance = AC= 3*6^0.5 = 7.35
(b)
direction = (-1,1,2)
(c)
t = 3 hrs
(d)
interception point A = (-1,0,7)
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