Question

Two points $(1,-1,1)$ and $(-2,0,5)$ with respect to the plane $2x+3y-z+7=0$ lie on

• A. opposite sides
• B. same side
• C. on the plane
• D. in side the plane

Answer 1

The correct option is A opposite sides

We determine the product of the perpendicular distances of the $2$ points from the plane.
If it's negative they lie on the opposite side. If it's positive they lie on the same side
if it's zero at least one of them lies on the plane.
On putting the values of coordinates in the distance formula, we get $\left(5\right)\times (-2)=-10<0.$
Hence, they lie on the opposite sides.