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,bc) and the foot of perpendicular from point Q to the 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).
`:." "0+Bb+Cc=0`
`and" "Aa+0+Cc=0`
`rArr" "Cc=BbandCc=-Aa`
`:." "-Aa=-Bb=Cc=k`
`rArr" "A=-(k)/(a),B=-(k)/(b)andC=(k)/(c)`
From Eq. (i), `-(k)/(a)x-(k)/(b)y+(k)/(c)z=0`
`rArr" "-(x)/(a)-(y)/(b)+(z)/(c)=0or(x)/(a)+(y)/(b)-(z)/(c)=0`