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There are two lines:

L1 : x = 1 + 2t ; y = 2 - t ; z = -1 + 3t.

L2: x = 2 - 3m ; y = 2m ; z = 1 - m.

The problem states to find a general point on A on L1 and a general point B on L2, and then find the vector AB from those points.

Hence,

Vector AB = ( -3m - 2t - 1 , 2m + t - 2, -m -3t +2).

Then, the problem states to find specific points A and B such that vector AB is parallel to the product of direction vectors of lines L1 and L2.

using determinants, the product of direction vectors come out to be (-5,-7,1). I'm pretty sure it is. This also means that direction vector of vector AB has to be either (-5, -7, 1) or scalar multiples of it. But when I equate

-3m-2t-1 = -5

2m + t - 2 = -7

-m -3t +2 = 1

and do simultaneous equation, the value for m and t doesn't come out to be right. if it works for x and y, it doesnt' work for z, and so on.

…..additional info after not getting the first one responded

Here's what I meant by product of direction vectors.

direction vector L1 = (2,-1,3)

direction vector L2 = (-3,2,-1)

Thus D.V. L1 * D.V. L2 = det( i j k ) = (-5,-7,1)

......................................( 2 -1 3 )

..................................... ( -3 2 -1 )

forgive me for using parenthesis where abstract value sign should be.

At any rate, that's what I meant by product.

if you pictured it correctly that it's the "cross product", that's what I originally figured: that since product of direction vector is perpendicular to the lines connecting the two "general points", it cannot be parallel. but I can't imagine that the problem is flawed because it is coming straight out of the infamous International Baccalaureate internal assessment sheet! So, here's the dilemma. I think I'm interpreting the problem in a wrong direction.

Since I really can't see what to do, I'll just present the full problem here:

Consider the two lines:

L1 : x = 1 + 2t ; y = 2 - t ; z = -1 + 3t.

L2: x = 2 - 3m ; y = 2m ; z = 1 - m.

4) Given that l-1 and l-2 are direction vectors for lines L1 and L2, find the vector product l-1 x l-2.

5) Taking a general point A on L1 and a general point B on L2, find the vector AB.

6) Find points A and B such that AB is parallel to l-1 x l-2.

7) Find the magnitude of vector AB.

....

As noted before, vector product, if I did things correctly, should be (-5,-7,1).

Number 5's answer, I believed, was

Vector AB = ( -3m - 2t - 1 , 2m + t - 2, -m -3t +2).

As I stated before in the question.

Number 6 is the point where I have trouble with- the way it is worded, it sounds as if two points each in Line L1 and L2 are supposed to be parallel to their direction vector products. I stared at the problem for 20 minutes, and yelled out, "THIS DOES NOT MAKE SENSE."

I'm really sorry that I had to resort to actually presenting a problem, but

please understand that I tried my best and even more.

Thank you so much.

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# Homework Help: Parallel Vectors Problem

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