Vectors question D:

[simba]

Hey guys!
I'm completely stuck on part D of this question! I've come across questions similar to part D before and have never figured out how to solve it so any help would be super massively appreciated!! Thank you!

[SocialRhubarb]

Path of fighter =

Position vector of fighter =

When the fighter is closest to the station, the direction of its motion will be perpendicular to its position vector.









Position vector of fighter =



I think I may have made a mistake, since I think the point I've calculated is before the starting point.

It also actually doesn't specify that the fighter is travelling in a straight line.

[Alwin]

Hey guys!
I'm completely stuck on part D of this question! I've come across questions similar to part D before and have never figured out how to solve it so any help would be super massively appreciated!! Thank you!

Assuming it's travelling in a straight line:

Parts a,b,c

a)
b)
c)

d) Shortest distance when the direction of motion and the position vector at right angles



Hmm, as you can see I got something much more different...

Did 42/9 wrong.. thanks rhubarb. And yes, i finally got W|A to like me and verified your answer (which i now finally agree with ) is correct.

EDIT #1515345: thanks duquesne9995 for finding another mistake i make

[SocialRhubarb]

d)



Hmm, as you can see I got something much more different...

That may be your reason.

[Alwin]

That may be your reason.

I know, and that's the point.

8i - 4j + 13k + (6i - 12j + 12k) m   and  8i - 4j + 13k + (i - 2j + 2k) m are the same, but give different answers in the end

also W|A ain't working for me tonight for some reason. Anyone know how to find the distance between the point (0,0,0) and line (8,-4,13)+(6,-12,12)t on W|A ? That why we can verify the answer...
Either that or the OP could tell us

[SocialRhubarb]

No, as in, look carefully. That's an error in working. You're missing a factor of 3.

I think the two answers will be the same once rectified.

[Alwin]

No, as in, look carefully. That's an error in working. You're missing a factor of 3.

I think the two answers will be the same once rectified.

*facepalm*

I also found 3 more mistakes like -4+28/9 = -22/9... remind me never to do maths after a practise english exam

TY Rhubarb ^^

[duquesne9995]

It also actually doesn't specify that the fighter is travelling in a straight line.

Assuming it's travelling in a straight line:

Hi guys I was thinking that since the question says "a jet fighter flying with constant speed" that may imply that the position is linear! 

Someone tell me if I'm wrong.

[simba]

Thank you all so much for the help! The answer in the textbook is 10/3i+16/3j+11/3k

[lzxnl]

Hi guys I was thinking that since the question says "a jet fighter flying with constant speed" that may imply that the position is linear! 

Someone tell me if I'm wrong.

Think circle.

[SocialRhubarb]

Constant velocity would imply a linear path.

[lzxnl]

Hi guys I was thinking that since the question says "a jet fighter flying with constant speed" that may imply that the position is linear! 

Someone tell me if I'm wrong.

[simba]

Just one more question, how did you actually create the position vector of the fighter? I wouldn't have thought to write that equation at all! Is there any formula or way to determine a position vector? Thank you

[Alwin]

Just one more question, how did you actually create the position vector of the fighter? I wouldn't have thought to write that equation at all! Is there any formula or way to determine a position vector? Thank you

it's kinda common sense... sorry if that makes you feel bad! but then again it's taught in both the MUEP and UMEP maths courses.

Anyways here's a pretty diagram to try help explain it

Think circle.

Yes a circle does work since it says constant speed. Actually, so does any random path so long as it maintains a constant speed.
@Rhubarb, you're right if the question said constant velocity, then it's linear

But let's all pretend it's linear and duquesne is right  -makes our lives a whole lot easier. Or nliu, find the circular path and solve it for us (infinite soln if its circular i think)

[simba]

Thanks for the help! I struggle pretty badly with vectors (not sure why) so most things that are probably pretty obvious don't really click for me.. Hopefully with plenty of revision that will change though!