Let the line (x-3)/7=(y-2)/(-1)=(z-3)/(-4) intersect the plane containing the lines (x-4)/1=(y+1)/(-2)=z/1 and 4 a x-y+5 z-7 a=0=2 x-5 y-z-3, a R at the point P(α, β, γ). Then the value of α+β+γ equals _ _ _ _ _ _ _.

Three Dimensional Geometry: JEE Main 2022 Mathematics question

JEE Main 2022 · 27 Jul, Morning shift · Q25

JEE Main 202227 Jul, Morning shiftMathematicsMediumThree Dimensional Geometry249× since 2002

Let the line

\frac{x-3}{7}=\frac{y-2}{-1}=\frac{z-3}{-4}

intersect the plane containing the lines

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

and

4 a x-y+5 z-7 a=0=2 x-5 y-z-3, a \in \mathbb{R}

at the point

P(\alpha, \beta, \gamma)

. Then the value of

\alpha+\beta+\gamma

equals _____________.

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