jee-main 2022 Q79

jee-main · India · session1_26jun_shift1 Vectors 3D & Lines Plane Rotation About a Line
Let the plane $2 x + 3 y + z + 20 = 0$ be rotated through a right angle about its line of intersection with the plane $x - 3 y + 5 z = 8$. If the mirror image of the point $\left( 2 , - \frac { 1 } { 2 } , 2 \right)$ in the rotated plane is $B ( a , b , c )$, then
(1) $\frac { a } { 8 } = \frac { b } { 5 } = \frac { c } { - 4 }$
(2) $\frac { a } { 4 } = \frac { b } { 5 } = \frac { c } { - 2 }$
(3) $\frac { a } { 8 } = \frac { b } { - 5 } = \frac { c } { 4 }$
(4) $\frac { a } { 4 } = \frac { b } { 5 } = \frac { c } { 2 }$
Let the plane $2 x + 3 y + z + 20 = 0$ be rotated through a right angle about its line of intersection with the plane $x - 3 y + 5 z = 8$. If the mirror image of the point $\left( 2 , - \frac { 1 } { 2 } , 2 \right)$ in the rotated plane is $B ( a , b , c )$, then\\
(1) $\frac { a } { 8 } = \frac { b } { 5 } = \frac { c } { - 4 }$\\
(2) $\frac { a } { 4 } = \frac { b } { 5 } = \frac { c } { - 2 }$\\
(3) $\frac { a } { 8 } = \frac { b } { - 5 } = \frac { c } { 4 }$\\
(4) $\frac { a } { 4 } = \frac { b } { 5 } = \frac { c } { 2 }$