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Q.
The angle between the lines $2x = 3y = - z$ and $6x = - y = - 4z$ is
Three Dimensional Geometry
Solution:
The given equations can be rewritten as
$\frac{x}{3}=\frac{y}{2}=\frac{z}{-6}$ and $\frac{x}{2}=\frac{y}{-12}=\frac{z}{-3}$
$\therefore $ Angle between the lines is given by
$cos\,\theta=\frac{6-24+18}{\sqrt{9+4+36}\sqrt{4+144+9}}$
$=\frac{0}{\sqrt{49}\sqrt{157}}=0$
$\Rightarrow \theta=90^{\circ}$