The equation of the plane through the point (1, 2, 3), (-1,4, text 2) and (3, 1,1) is:

Question

The equation of the plane through the point (1, 2, 3), (-1,4, text 2) and (3, 1,1) is: (A)  5x+y+12z-23=0  (B)  5x+6y+ text 2z-23=0  (C)  x+ text 6y+ text 2z-13=0  (D)  x+y+2-13=0

Tardigrade Admin · Accepted Answer

Equation of plane through (1, 2, 3) is a(x-1)+b(y-2)+c(z-3)=0 ...(i) It passes through (-1, 4, 2) and (3, 1, 1) -2a+2b-c=0 ...(ii) and 2a-b-2c=0 ...(iii) From Eqs. (ii) and (iii) (a/-5)=(b/-6)=(c/-2) ∴ Equation of plane is -5x-6y-2z+5+12+6=0 ⇒ 5x+6y+2z-23=0

Q. The equation of the plane through the point (1, 2, 3), $(- 1, 4, 2)$ and (3, 1,1) is:

$5 x + y + 12 z - 23 = 0$

$5 x + 6 y + 2 z - 23 = 0$

$x + 6 y + 2 z - 13 = 0$

$x + y + 2 - 13 = 0$

$5 x + y + z - 23 = 0$

Q. The equation of the plane through the point (1, 2, 3), (−1,4,2) and (3, 1,1) is:

5x+y+12z−23=0

5x+6y+2z−23=0

x+6y+2z−13=0

x+y+2−13=0

5x+y+z−23=0