Show that the lines $\cfrac{{x - 5}}{7} = \cfrac{{y + 2}}{{ - 5}} = \cfrac{z}{1}$ and $\cfrac{x}{1} = \cfrac{y}{2} = \cfrac{z}{3}$ are perpendicular to each other.
Show that the lines $\cfrac{{x - 5}}{7} = \cfrac{{y + 2}}{{ - 5}} = \cfrac{z}{1}$ and $\cfrac{x}{1} = \cfrac{y}{2} = \cfrac{z}{3}$ are perpendicular to each other.
Official Solution
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. : Direction ratios of the given lines are respectively
$< 7, - 5,1 >$ and $< 1,2,3 >$.
Since $7 \times 1 + ( - 5) \times 2 + 1 \times 3 = 0$
therefore , the given lines are perpendicular.
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