jee-main 2021 Q80

jee-main · India · session4_31aug_shift1 Vectors: Lines & Planes Find Cartesian Equation of a Plane

Let the equation of the plane, that passes through the point $( 1,4 , - 3 )$ and contains the line of intersection of the planes $3 x - 2 y + 4 z - 7 = 0$ and $x + 5 y - 2 z + 9 = 0$, be $\alpha x + \beta y + \gamma z + 3 = 0$, then $\alpha + \beta + \gamma$ is equal to :
(1) $- 15$
(2) 15
(3) $- 23$
(4) 23

Let the equation of the plane, that passes through the point $( 1,4 , - 3 )$ and contains the line of intersection of the planes $3 x - 2 y + 4 z - 7 = 0$ and $x + 5 y - 2 z + 9 = 0$, be $\alpha x + \beta y + \gamma z + 3 = 0$, then $\alpha + \beta + \gamma$ is equal to :\\
(1) $- 15$\\
(2) 15\\
(3) $- 23$\\
(4) 23

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