Wondered if anyone can help me with a maths problem?

#1

Sorry, didn’t know if this should go into Visuals, or just general. But I am currently working my way through the book Computer Graphics Mathematical First Steps and wondered if anyone could help on a question I have. (It is the final part of question 6.5 on p77 if anyone has the book): it’s on Vector Equations…

Find the vector equation of the straight line that passes through P(-4, 1, 2) and R(2, 7, 6) in which the parameter u takes the value 0 at Q, the midpoint of PR and value 1 at R. (I have managed to do the first answer up to here - r= (-1 + 3 u)i + (4 + 3u)j + (4 + 2u)k. but it is the next part I struggle with) - Calculate the length of QR and hence find the vector equation of this line using the parameter v where v = 0 at Q and v measures length along the line.

the answer is r = (-1 + 0.64v)i + (4 + 0.64v)j + (4 + 0.43v)k

If you can help I would greatly appreciate it. I just can’t see how you get to this answer.

Thanks if anyone can help, sorry if this is completely inappropriate to the forum…

#2

Did you ever figure this one out? If not, then here is what I think they are looking for…

In part 1 you figured out an equation for the line from Q -> R.
When you use a value of 0 in that equation you get the point Q, and when you use the value 1 you get the point R.

Now what they want you do do is modify part of your equation so that when you substitute in 0 then you still get point Q, but when you substitute in 1 you get a point 1 unit away from point Q in the direction of R. Doing this will still leave you with the same line though…it will still go through both of Q and R…it’s just that now the value you put in conveniently gives you a point at that exact distance away from Q.

To do that you just need to figure out the length of your current line…which you do by finding the square root of the sum of squares. i.e. sqrt of (3^2 + 3^2 + 2^2), or about 4.69.

Then you divide by that number and that’s how you get those numbers in your final equation. (3 / 4.69) = 0.64 and (2 / 4.69) = 0.43

Hopefully that all makes sense :):

#3

No I never figured it out. But that makes perfect sense! I haven’t got the book with me so can’t go over it but thank you for that help i really appreciate it.

Suppose i should get back to studying it, now i fully understand it!

thanks again

#4

A very interesting question!
Thank you for posting the solution GoLeafsGo