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The shortest distance between the lines `x/(-3)=(y-1)/1=(z+1)/(-1)a n d(x-2)/1=(y-3)/2=((z+(13//7))/(-1))` is zero. Statement 2: The given lines are perpendicular.

A

Both the statements are true, and Statement 2 is the correct explanation for Statement 1.

B

Both the Statements are true, but Statement 2 is not the correct explanation for Statement 1.

C

Statement 1 is true and Statement 2 is false.

D

Statement 1 is false and Statement 2 is true.

Text Solution

Verified by Experts

The correct Answer is:
d
Direction ratios of the given lines are `(-3, 1, -1) and (1, 2, -1)`. Hence, the lines are perpendicular as `(-3)(1)+ (1)(2)+ (-1)(-1)=0`.
Also lines are coplanar as
`" "|{:(0-2,,1-3,,-1+(13//7)),(-3,,1,,-1),(1,,2,,-1):}|=0`
But Statement 2 is not enough reason for the shortest distance to be zero, as two skew lines can also be perpendicular.
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