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The equation of the plane through P(x(1)...

The equation of the plane through `P(x_(1),y_(1),z_(1))` and perpendicular to OP, (O being the origin) is

A

`x x_(1)+yy_(1)+zz_(1)=x_(1)+y_(1)`

B

`x x_(1)+yy_(1)+zz_(1)=y_(1)+z_(1)`

C

`x x_(1)+yy_(1)+zz_(1)=x_(1)^(2)+y_(1)^(2)+z_(1)^(2)`

D

`x x_(1)+yy_(1)=z+z_(1)`

Text Solution

Verified by Experts

The correct Answer is:
C
The equation of plane in normal from is
`(x x_(1))/(sqrt(x_(1)^(2)+y_(1)^(2)+z_(1)^(2)))+(yy_(1))/(sqrt(x_(1)^(2)+y_(1)^(2)+z_(1)^(2)))+(zz_(1))/(sqrt(x_(1)^(2)+y_(1)^(2)+z_(1)^(2)))sqrt(x_(1)^(2)+y_(1)^(2)+z_(1)^(2))`
`:." "x x_(1)+yy_(1)+zz_(1)=x_(1)^(2)+y_(1)^(2)+z_(1)^(2)`
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