Question

Given lines $\frac{x-4}{2}=\frac{y+5}{4}=\frac{z-1}{-3}$ and $\frac{x-2}{1}=\frac{y+1}{3}=\frac{z}{2}$
Statement 1 : The lines intersect.
Statement 2: They are not parallel

• A. Statement 1 is true, statement 2 is true and statement 2 is correct explanation for statement 1
• B. Statement 1 is true, statement 2 is true and statement 2 is not correct explanation for statement 1
• C. Statement 1 is true, statement 2 is false
• D. Statement 1 is false, statement 2 is true

Answer 1

Answer: (C)

Statement 1 is true, statement 2 is false

$\frac{x-4}{2}=\frac{y+5}{4}=\frac{z-1}{-3}$

$\frac{x-4}{2}=\frac{y+5}{4}$

$y=2x-13$

$y-2x+13=\frac{z-1}{-3}$

$x=-\frac{-3y-z-38}{6}$

$6x=3y+z+38$

$6x-3y-z=38$...(1)

$\frac{x-2}{1}=\frac{y+1}{3}=\frac{z}{2}$

$\frac{x-2}{1}=\frac{y+1}{3}$

$y=3x-7$

$y-3x+7=\frac{z}{2}$

$x=-\frac{z-2y-14}{6}$

$6x=-z+2y+14$

$6x-2y+z=14$...(2)

Therefore (1) and (2) intersect each other.