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  4. 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.

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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.

Vector Algebra

Solution:

$L_1$ and $L_2$ are obviously not parallel
Consider the determinant
$D =\begin{vmatrix}2 & -4 & 1 \\ 2 & 4 & -3 \\ 1 & 3 & 2\end{vmatrix}=2(8+9)+4(4+3)+1(6-4)=34+28+2 \Rightarrow D \neq 0 \Rightarrow$ skew