Let the plane P: r. a = d contain the line of intersection of two planes r. (i + 3 j - k) = 6 and r. (- 6 i + 5 j - k) = 7. If the plane P passes through the point (2,3,1/2), then the value of (|13 a |²)/(d²) is equal to:

Three Dimensional Geometry: JEE Main 2022 Mathematics question

JEE Main 2022 · 28 Jun, Morning shift · Q2443

JEE Main 202228 Jun, Morning shiftMathematicsMediumThree Dimensional Geometry249× since 2002

Let the plane

P:\overrightarrow r \,.\,\overrightarrow a = d

contain the line of intersection of two planes

\overrightarrow r \,.\,\left( {\widehat i + 3\widehat j - \widehat k} \right) = 6

and

\overrightarrow r \,.\,\left( { - 6\widehat i + 5\widehat j - \widehat k} \right) = 7

. If the plane P passes through the point

\left( {2,3,{1 \over 2}} \right)

, then the value of

{{|13\overrightarrow a {|^2}} \over {{d^2}}}

is equal to :