The line of shortest distance between the lines (x-2)/0=(y-1)/1=z/1 and (x-3)/2=(y-5)/2=(z-1)/1 makes an angle of cos ⁻¹(√(2/27)) with the plane P: a x-y-z=0, (a>0). If the image of the point (1,1,-5) in the plane P is (α, β, γ), then α+β-γ is equal to _ _ _ _ _ _ _ _ _.

Three Dimensional Geometry: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jul, Morning shift · Q22

JEE Main 202225 Jul, Morning shiftMathematicsHardThree Dimensional Geometry249× since 2002

The line of shortest distance between the lines

\frac{x-2}{0}=\frac{y-1}{1}=\frac{z}{1}

and

\frac{x-3}{2}=\frac{y-5}{2}=\frac{z-1}{1}

makes an angle of

\cos ^{-1}\left(\sqrt{\frac{2}{27}}\right)

with the plane

\mathrm{P}: \mathrm{a} x-y-z=0

(a>0)

. If the image of the point

(1,1,-5)

in the plane

P

(\alpha, \beta, \gamma)

, then

\alpha+\beta-\gamma

is equal to _________________.

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