Question

( begin{aligned} 2 x &=3 y=-2 Rightarrow frac{x}{1 / 2}=frac{y}{1 / 3}=frac{2}{-1} 6 x=-y &=-4 z Rightarrow frac{x}{1 / 4}=frac{y}{-1}=frac{2}{-1 / 4} cos theta &=frac{left(frac{1}{2}+frac{1}{3},-1right) cdotleft(frac{1}{6},-1,-frac{1}{4}right)}{sqrt{frac{1}{9}+frac{1}{4}+1} sqrt{frac{1}{36}+frac{1}{16}+1}} &=frac{frac{1}{12}-frac{1}{3}+frac{1}{4}}{sqrt{frac{4+9+36}{36}} sqrt{frac{4+9+144}{36 times 16}}} cos theta=& 0 Rightarrowleft|frac{9}{2}right| end{aligned} )

# 1. Find the angle between the lines 2x = 3y = -z and 6x = - y = - 4z.

Solution