Let the plane passing through the point (-1,0,-2) and perpendicular to each of the planes 2 x+ y- z=2 and x-y-z=3 be a x+ b y+ c z+8=0. Then the value of a+b+c is equal to:

Question

Let the plane passing through the point (-1,0,-2) and perpendicular to each of the planes 2 x+ y- z=2 and x-y-z=3 be a x+ b y+ c z+8=0. Then the value of a+b+c is equal to: (A) 3 (B) 8 (C) 5 (D) 4

Tardigrade Admin · Accepted Answer

Normal of req. plane (2 hati+ hatj- hatk) ×( hati- hatj- hatk) =-2 hati+ hatj-3 hatk Equation of plane -2(x+1)+1(y-0)-3(z+2)=0 -2 x+y-3 z-8=0 2 x-y+3 z+8=0 a +b +c=4

Q. Let the plane passing through the point $(- 1, 0, - 2)$ and perpendicular to each of the planes $2 x + y - z = 2$ and $x - y - z = 3$ be $a x + b y + cz + 8 = 0$ . Then the value of $a + b + c$ is equal to:

3

8

5

4

Normal of req. plane $(2 \hat{i} + \hat{j} - \hat{k}) \times (\hat{i} - \hat{j} - \hat{k})$ $= - 2 \hat{i} + \hat{j} - 3 \hat{k}$
Equation of plane
$- 2 (x + 1) + 1 (y - 0) - 3 (z + 2) = 0$
$- 2 x + y - 3 z - 8 = 0$
$2 x - y + 3 z + 8 = 0$
$a + b + c = 4$

Q. Let the plane passing through the point (−1,0,−2) and perpendicular to each of the planes 2x+y−z=2 and x−y−z=3 be ax+by+cz+8=0. Then the value of a+b+c is equal to:

3

8

5

4

Normal of req. plane (2i^+j^​−k^)×(i^−j^​−k^) =−2i^+j^​−3k^ Equation of plane −2(x+1)+1(y−0)−3(z+2)=0 −2x+y−3z−8=0 2x−y+3z+8=0 a+b+c=4

Q. Let the plane passing through the point $(- 1, 0, - 2)$ and perpendicular to each of the planes $2 x + y - z = 2$ and $x - y - z = 3$ be $a x + b y + cz + 8 = 0$ . Then the value of $a + b + c$ is equal to:

Normal of req. plane $(2 \hat{i} + \hat{j} - \hat{k}) \times (\hat{i} - \hat{j} - \hat{k})$ $= - 2 \hat{i} + \hat{j} - 3 \hat{k}$
Equation of plane
$- 2 (x + 1) + 1 (y - 0) - 3 (z + 2) = 0$
$- 2 x + y - 3 z - 8 = 0$
$2 x - y + 3 z + 8 = 0$
$a + b + c = 4$