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 $
• E. $ 5x+y+z-23=0 $

Answer 1

Answer: (B)

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) $ \frac{a}{-5}=\frac{b}{-6}=\frac{c}{-2} $ $ \therefore $ Equation of plane is $ -5x-6y-2z+5+12+6=0 $
$ \Rightarrow $ $ 5x+6y+2z-23=0 $