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The equation of two straight lines ar...

The equation of two straight lines are `(x-1)/2=(y+3)/1=(z-2)/(-3)a n d(x-2)/1=(y-1)/(-3)=(z+3)/2dot` Statement 1: the given lines are coplanar. Statement 2: The equations `2x_1-y_1=1,x_1+3y_1=4a n d3x-1+2y_1=5` are consistent.

A

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement-2 is True.

Text Solution

Verified by Experts

The coordinates of arbitrary positions of the given lines are `(2r+1,r-3,-3r+2)` and `(s+2,-3s+1,2s-3)` respectively.
Given lines will intersect (be coplanar) if
`2r+1=s+2,r-3=-3s+1` and `-3r+2=2s-3`
are conistent i.e `2r-s=1,r+3s=4` and `3r+2s=5` are consistent.
Clearly, values of `r` and `s` obtain from any two equations satisfy the third equation. So, these equations are consistent.
Hence, both the statements are true and statement -2 is a correct explanation for statement -1.
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