If the foot of the perpendicular from the origin to plane is `P(a ,b ,c)` , the equation of the plane is a. `x/a=y/b=z/c=3` b. `a x+b y+c z=3` c. `a x+b y+c z=a^(I2)+b^2+c^2` d. `a x+b y+c z=a+b+c`

Options

A. `(x)/(a)+(y)/(b)+(z)/(c)=3`
B. `ax+by+cz=3`
C. `ax+by+cz=a^(2)+b^(2)+c^(2)`
D. `ax+by+cz=a+b+c`

Answer

c

Explanation

Direction ratios of OP are (a,b,c) Therefore, equation of the plane is
`a(x-a)+b(y-b)+c(z-c)=0`
i.e., `xa+yb+zc=a^(2)+b^(2)+c^(2)`