Question

Assertion (A): The points $(2,1,5)$ and $(3,4,3)$ lie on opposite side of the plane $2x+2y-2z-1=0$.
Reason (R): The algebraic perpendicular distance from the given points to the line have opposite sign.

• A. Both A and R are individually true and R is the correct explanation of A
• B. Both A and R individually true but R is not the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Answer 1

The correct option is A Both A and R are individually true and R is the correct explanation of A

The statement is true when two points

$A(x_1,y_1,z_1)$ and $B(x_2,y_2,z_2)$ lie on the opposite sides of a plane $P(x,y,z)=0$

Then $P(x_1,y_1,z_1)$ and $P(x_2,y_2,z_2)<0$

$A:$ The statement is true. points are $A(2,1,5),P(3,4,3)$

$\therefore P(2,1,5).P(3,4,5)=(-5)\left(7\right)<0$

Ans (a) option $i.e.$ Both A and R are individually true and R is the correct explanation of A