Let the equation of the plane passing through the line x-2 y-z-5=0=x+y+3 z-5 and parallel to the line x+y+2 z-7=0=2 x+3 y+z-2 be a x+b y+c z=65. Then the distance of the point (a, b, c) from the plane 2 x+2 y-z+16=0 is

Question

Let the equation of the plane passing through the line x-2 y-z-5=0=x+y+3 z-5 and parallel to the line x+y+2 z-7=0=2 x+3 y+z-2 be a x+b y+c z=65. Then the distance of the point (a, b, c) from the plane 2 x+2 y-z+16=0 is  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Equation of plane is ( x -2 y - z -5)+ b ( x + y +3 z -5)=0 | 1+ b -2+ b -1+3 b 1 1 2 2 3 1|=0 ⇒ b =12 ∴ text plane is 13 x +10 y +35 z =65 Distance from given point to plane =9

Q. Let the equation of the plane passing through the line $x - 2 y - z - 5 = 0 = x + y + 3 z - 5$ and parallel to the line $x + y + 2 z - 7 = 0 = 2 x + 3 y + z - 2$ be $a x + b y + cz = 65$ . Then the distance of the point $(a, b, c)$ from the plane $2 x + 2 y - z + 16 = 0$ is _______

Equation of plane is
$(x - 2 y - z - 5) + b (x + y + 3 z - 5) = 0$
$∣ ∣ 1 + b 12 - 2 + b 13 - 1 + 3 b 21 ∣ ∣ = 0$
$\Rightarrow b = 12$
$∴ plane is 13 x + 10 y + 35 z = 65$
Distance from given point to plane $= 9$

Q. Let the equation of the plane passing through the line x−2y−z−5=0=x+y+3z−5 and parallel to the line x+y+2z−7=0=2x+3y+z−2 be ax+by+cz=65. Then the distance of the point (a,b,c) from the plane 2x+2y−z+16=0 is _______

Equation of plane is (x−2y−z−5)+b(x+y+3z−5)=0 ∣∣​1+b12​−2+b13​−1+3b21​∣∣​=0 ⇒b=12 ∴ plane is 13x+10y+35z=65 Distance from given point to plane =9

Q. Let the equation of the plane passing through the line $x - 2 y - z - 5 = 0 = x + y + 3 z - 5$ and parallel to the line $x + y + 2 z - 7 = 0 = 2 x + 3 y + z - 2$ be $a x + b y + cz = 65$ . Then the distance of the point $(a, b, c)$ from the plane $2 x + 2 y - z + 16 = 0$ is _______

Equation of plane is
$(x - 2 y - z - 5) + b (x + y + 3 z - 5) = 0$
$∣ ∣ 1 + b 12 - 2 + b 13 - 1 + 3 b 21 ∣ ∣ = 0$
$\Rightarrow b = 12$
$∴ plane is 13 x + 10 y + 35 z = 65$
Distance from given point to plane $= 9$