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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

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
Any point on the first line is `(2x_(1)+1, x_(1)-3, -3x_(1)+2)`.
Any point on the second line is `(y_(1)+2, -3y_(1) +1, 2y_(1)-3)`.
If two lines are coplanar, then `2x_(1)-y_(1)=1, x_(1)+3y_(1)=4 and 3x_(1)+ 2y_(1)= 5` are consistent.
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