- #1
deanchhsw
- 14
- 0
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.
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 :(
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 :(