help with maths problem please

**Juli26** · February 08, 2011, 11:22 AM

I will post a picture with symbols because I didn't know how to write them in english.

If it's not clear at the end d1 touches d2 and the equation of d2 is that in the pic.

**Randarkmaan** · February 08, 2011, 02:24 PM

It's a vector cross product right?
M is a point? a is a vector [2,3,1]? Or is that thing to the right a one-column matrix?

Though, I can't really see exactly what it is that you're after here (yes, I see it is 'what is d?'),
could you perhaps try to explain the problem you were given?

**Juli26** · February 08, 2011, 02:48 PM

sorry for giving details that are not clear.
find the line (d). M is a point which is part of that line. The line is perpendicular with the vector (a)
and the line crosses another line (d2) which has that equation.

I hope I was clear but like I said I don't know the terms in english.

P.S. I forgot to say that this situation is in space, not in a plan.

**Randarkmaan** · February 08, 2011, 03:01 PM

OK, that's alot clearer.

You should start with looking at the fact that d is perpendicular to vector a, that means that the dot product of the direction vector of d and vector a should be zero. Ofcourse you have several choices here, but you will have one to settle on because of the line d2 that crosses d and the line includes the point M (better just make this the 'starting point' in the equation for that line).

Hope that helps somewhat, if that did not help, or you already tried this and got stranded, I'll solve it and see if I can give you another push (or just give you the answer, but I guess you already have that?)

EDIT: You may want to look at crossproduct of the direction vectors d1 and d2. It might be useful (or not). I haven't done done the problem, had a look at it, and it became a little messy so I decided to have a look at it tomorrow.

**Juli26** · February 08, 2011, 04:02 PM

I have already tried different solutions but every time I get stuck at some point. Thx for the help anyway. If you can solve this for me though you would do me a great favor since tomorrow I have an exam and that exercise is the only one I can't do right now (I have to admit I was very careless during the semester and didn't read that much till now at the season of exams)

**Randarkmaan** · February 09, 2011, 02:18 AM

Ok, I have solved it

Are you familiar with the equations for planes? Because the key is there.
What you should do is define a plane that includes the point M, and has vector a as its normal vector. d2 will intersect this plane in a point, then you define a vector from M to this point. That will be d1's direction vector.
This should give you the solution, I've gone over it a few times to see if I went wrong somewhere, and I couldn't find anything alarming.

Good luck, hope it was not too late. I'm really sorry if it was though, last night was a little late for math problems, sorry