For real numbers α and β ≠ 0, if the point of intersection of the straight lines (x - α)/1 = (y - 1)/2 = (z - 1)/3 and (x - 4)/(β) = (y - 6)/3 = (z - 7)/3, lies on the plane x + 2y - z = 8, then α - β is equal to:

Three Dimensional Geometry: JEE Main 2021 Mathematics question

JEE Main 2021 · 27 Jul, Evening shift · Q2433

JEE Main 202127 Jul, Evening shiftMathematicsMediumThree Dimensional Geometry249× since 2002

For real numbers

\alpha

and

\beta

\ne

0, if the point of intersection of the straight lines

{{x - \alpha } \over 1} = {{y - 1} \over 2} = {{z - 1} \over 3}

and

{{x - 4} \over \beta } = {{y - 6} \over 3} = {{z - 7} \over 3}

, lies on the plane x + 2y

-

z = 8, then

\alpha

-

\beta

is equal to :