Let P be a plane passing through the points (1, 0, 1), (1, - 2, 1) and (0, 1, - 2). Let a vector a = α i + β j + γ k be such that a is parallel to the plane P, perpendicular to (i + 2 j + 3 k) and a. (i + j + 2 k) = 2, then (α - β + γ)² equals _ _ _ _ _ _.

Three Dimensional Geometry: JEE Main 2021 Mathematics question

JEE Main 2021 · 20 Jul, Morning shift · Q25

JEE Main 202120 Jul, Morning shiftMathematicsHardThree Dimensional Geometry249× since 2002

Let P be a plane passing through the points (1, 0, 1), (1,

-

2, 1) and (0, 1,

-

2). Let a vector

\overrightarrow a = \alpha \widehat i + \beta \widehat j + \gamma \widehat k

be such that

\overrightarrow a

is parallel to the plane P, perpendicular to

(\widehat i + 2\widehat j + 3\widehat k)

and

\overrightarrow a \,.\,(\widehat i + \widehat j + 2\widehat k) = 2

, then

{(\alpha - \beta + \gamma )^2}

equals ____________.

Your answerType your answer. Integers and decimals are accepted.