There are two lines:(adsbygoogle = window.adsbygoogle || []).push({});

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.

Then, how do you solve this problem? I have spent nearly 20 minutes on this, and it's driving me crazy! nuts! math genies, please help :(

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# Problems with parallel vectors

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