Common perpendicular of two lines

AI Thread Summary
To find the common perpendicular between the two lines defined by the equations x / 2 = (y-1) / 2 = z and x + 1 = y – 2 = (z + 4) / 2, the direction vectors are identified as V1 = (2, 2, 1) and V2 = (1, 1, 2). The cross product of these direction vectors, calculated as V1 X V2, results in (3, -3, 0). This confirms the correctness of the calculation, indicating that the common perpendicular can be determined using this vector. The initial confusion regarding the distance being zero is clarified through this vector analysis. The discussion concludes with the affirmation of the cross product's accuracy.
ydan87
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Hi there,
The two given lines:
1) x / 2 = (y-1) / 2 = z
2) x + 1 = y – 2 = (z + 4) / 2
I need to find the common perpendicular between them.
Though when I tried to calculate the distance between them, I get 0.

Can someone please help?

Thanks in advance
 
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Think about the cross product of their direction vectors.
 
Easier than I thought! Thanks :)
 
Direction vectors of lines 1 and 2: V1 = (2, 2, 1), V2 = (1, 1, 2)
V1 X V2 = (3, -3, 0)

Is it correct?
 
Yes, it is.
 

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