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

Question

Given lines (x-4/2)=(y+5/4)=(z-1/-3) and (x-2/1)=(y+1/3)=(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 the correct explanation for statement-1. (C) Statement-1 is true, statement-2 is false. (D) Statement-1 is false, statement-2 is true.

Tardigrade Admin · Accepted Answer

L1 and L2 are obviously not parallel Consider the determinant D =|2 -4 1 2 4 -3 1 3 2|=2(8+9)+4(4+3)+1(6-4)=34+28+2 ⇒ D ≠ 0 ⇒ skew

Q. 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.

Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.

Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.

Statement-1 is true, statement-2 is false.

Statement-1 is false, statement-2 is true.

$L_{1}$ and $L_{2}$ are obviously not parallel
Consider the determinant
$D = ∣ ∣ 221 - 4 43 1 - 3 2 ∣ ∣ = 2 (8 + 9) + 4 (4 + 3) + 1 (6 - 4) = 34 + 28 + 2 \Rightarrow D \neq = 0 \Rightarrow$ skew

Q. Given lines 2x−4​=4y+5​=−3z−1​ and 1x−2​=3y+1​=2z​ Statement-1: The lines intersect. Statement-2: They are not parallel.