SOLUTION: can anyone help with the following assignment question, Two aircrafts take off simultaneously from different airports. As they climb, their positions relative to an air traffic

Question 168322: can anyone help with the following assignment question,
Two aircrafts take off simultaneously from different airports. As they climb, their positions relative to an air traffic control centre t minutes later are given by the vectors:
r1 = 4i-30j +t(8i+2j+0.3k)
r2 = 12i+26j+ t(6i-3j+0.8k)
where i direction is due east, the j is due north and k is vertical distance and the units are kilometres.
a) find the coordinates of the point over the groun where the two planes cross
b) find also the difference in height and time that they both pass this point.
this is a completely different question to the examples we have done in the handouts and lessons so i am really struggling with this.
kevin
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
OK, let's break down the positions of each.

and similarly,

.
.
.
Now you have the position of both planes as a function of t.
.
.
.
When the planes cross, their i and j coordinates will be the same.

.
.
.

.
.
.
There is a problem.
For them to pass the same i,j point, the times need to match.
When t=4,

and similarly,

As you can see the x coordinates match, the y-coordinates don't.
The same thing happens at t=56/5.
There is no point in time when "i" positions and "j" positions match for the planes.
Please re-check the numbers and re-post.

RELATED QUESTIONS
Two planes set off simultaneously flying towards each other,from airports 900km apart.one (answered by stanbon)

10. Two aircrafts are flying straight towards each other, both aircraft are flying at a... (answered by harpazo)

Can anyone help me with this question? Please. Determine the rectangular coordinates for... (answered by Alan3354)

At what air speed must a plane be flown to complete a trip between two airports 420 miles (answered by ankor@dixie-net.com)

I have an assignment in my FINA class and I have tried to see what he is talking about,... (answered by solver91311)

This is the last question on my assignment and I'm stumped. Can anyone help? Thanks.... (answered by jim_thompson5910)

Hello! Iam having a problem with this part of an assignment for geography,if you could... (answered by richard1234)

Hi! Can you please help me to answer this question? The other day I was helping a... (answered by Fombitz)

How can confidence intervals be used to determine if the means of two populations are... (answered by stanbon)