Home
Class 12
MATHS
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.
Promotional Banner

Similar Questions

Explore conceptually related problems

The equation of two straight line are (x-1)/(2)=(y+3)/(1)=(z-2)/(-3) and (x-2)/(1)=(y-1)/(-3)=(z+3)/(2) Statement-I The given lines are coplanar. Statement-II The equation 2x_1-y_1=1, x_1+3y_1=4 and 3x_1+2y_1=5 are consistent.

The equations of two straight lines are (x-1)/2=(y+3)/1=(z-2)/(-3) and (x-2)/1=(y-1)/(-3)=(z+3)/2 Statement 1: The given lines are coplanar. Statement 2: The equations 2r-s=1 r+3s=4 3r+2s=5 are consistent.

The lines (x)/(1)=(y)/(2)=(z)/(3)and(x-1)/(-2)=(y-2)/(-4)=(z-3)/(-6) are

The lines (x-1)/1=(y-2)/2=(z-3)/(3) and (x-1)/1=y/3 =z/4 are

The vector equation of the straight line (1-x)/(3)=(y+1)/(-2)=(3-z)/(-1) is

Two lines (x)/(1)=(y)/(2)=(z)/(3)and(x+1)/(1)=(y+2)/(2)=(z+3)/(3) are

The lines (x-2)/(1)=(y-3)/(2)=(z-4)/(3)and(x-1)/(-5)=(y-2)/(1)=(z-1)/(1) are

Given lines (x-4)/(2)=(y+5)/(4)=(z-1)/(-3) and (x-2)/(1)=(y+1)/(3)=(z)/(2) Statement-I The lines intersect. Statement-II They are not parallel.