If A and B are foot of perpendicular drawn from point Q(a,b,c) to the planes yz and zx, then equation of plane through the point A,B, and O is

Options

A. `(x)/(a)+(y)/(b)-(z)/(c)=0`
B. `(x)/(a)-(y)/(b)+(z)/(c)=0`
C. `(x)/(a)-(y)/(b)-(z)/(c)=0`
D. `(x)/(a)+(y)/(b)+(z)/(c)=0`

Answer

A

Explanation

The foot of perpendicular from point Q(a,b,c) to the yz plane is A(0,b,c) and the foot of perpendicular from point Q to the foot of perpendicular from point Q to zx plane in B(a, 0, c).
Let the.equation of plane passing through the point (0, 0, 0) be
Ax+By+Cz=0 ... (i)
Also it is paring through the point A( 0, b, c) and B(a,0,c)
`therefore 0+Bc+C c=0`
`and Aa+0+C c=0`
`Rightarrow C c=Bb`
and `C c=-A a `
`therefore A=-(k)/(a), B=-(k)/(b)`
and `C=(k)/(c)`
From Eq. (i) , `(-k)/(a)x-(k)/(b)y+(k)/(c)z=0`
`Rightarrow -(x)/(a)-(y)/(b)+(z)/(c)=0 or (x)/(a)+(y)/(b)+(z)/(c)=0`