Line Intersection Triangle Area (Jee Mains)

Line Interactions and Distance

Hard

Line Intersection Triangle Area

Let A be the point of intersection of the lines
L₁ : $\frac{{x - 7}}{1}$ = $\frac{{y - 5}}{0}$ = $\frac{{z - 3}}{{ - 1}}$ and
L₂ : $\frac{{x - 1}}{3}$ = $\frac{{y + 3}}{4}$ = $\frac{{z + 7}}{5}$ . Let B and C be the point on the lines L₁ and L₂ respectively such that AB = AC = $\sqrt {15}$ . Then the square of the area of the triangle ABC is :

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