Let a line passing through the point (-1,2,3) intersect the lines L₁: (x-1)/3=(y-2)/2=(z+1)/(-2) at M(α, β, γ) and L₂: (x+2)/(-3)=(y-2)/(-2)=(z-1)/4 at N(a, b, c). Then, the value of ((α+β+γ)²)/((a+b+c)²) equals _ _ _ _ _.

Three Dimensional Geometry: JEE Main 2024 Mathematics question

JEE Main 2024 · 30 Jan, Evening shift · Q25

JEE Main 202430 Jan, Evening shiftMathematicsMediumThree Dimensional Geometry249× since 2002

Let a line passing through the point

(-1,2,3)

intersect the lines

L_1: \frac{x-1}{3}=\frac{y-2}{2}=\frac{z+1}{-2}

M(\alpha, \beta, \gamma)

and

L_2: \frac{x+2}{-3}=\frac{y-2}{-2}=\frac{z-1}{4}

N(a, b, c)

. Then, the value of

\frac{(\alpha+\beta+\gamma)^2}{(a+b+c)^2}

equals __________.

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