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Question:

Equation of the line of the shortest distance between the lines x1=y=z1 and x=y+1=z1 is :

x=y+1=z1

x1=y=z

x=y1=z2

x=y+1=z

Solution:

Since the line is perpendicular to both the given lines.D.R.'s of new line will be=∣∣∣∣∣^i^j^k1�𕒶1∣∣∣∣∣=(1)^i−(1)^j−(2)^kD.R.s of new line are=(1,−1,−2).Points of new line will be[(x2−x1),(y2−y1),(z2−z1)]=[(1−0),(−1−0),(0−0)]=(1,−1,0)Final equation will be x=y+1=z