Let A be the point of intersection of the lines L₁: (x-7)/1=(y-5)/0=(z-3)/(-1), and L₂: (x-1)/3=(y+3)/4=(z+7)/5. Let B and C be points on L₁ and L₂ respectively such that AB=AC=√(15). Then the square of the area of triangle ABC is:

Three Dimensional Geometry: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q119

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumThree Dimensional Geometry249× since 2002

Let

A

be the point of intersection of the lines

L_1:\;\frac{x-7}{1}=\frac{y-5}{0}=\frac{z-3}{-1},

and

L_2:\;\frac{x-1}{3}=\frac{y+3}{4}=\frac{z+7}{5}.

Let

B

and

C

be points on

L_1

and

L_2

respectively such that

AB=AC=\sqrt{15}

. Then the square of the area of triangle

ABC

is: