Answer
(a) The point $(0,0,10)$ does not lie in the plane $2x+y-z = 10$
(b) The point $(5,3,-3)$ does not lie in the plane $2x+y-z = 10$
(c) The point $(2,4,-2)$ lies in the plane $2x+y-z = 10$
(d) The point $(-3,6,-10)$ lies in the plane $2x+y-z = 10$
Work Step by Step
We can verify if the following points lie in the plane $2x+y-z = 10$
(a) $(0,0,10)$
$2(0)+(0)-(10) = -10$
The point $(0,0,10)$ does not lie in the plane $2x+y-z = 10$
(b) $(5,3,-3)$
$2(5)+(3)-(-3) = 10+3+3 = 16$
The point $(5,3,-3)$ does not lie in the plane $2x+y-z = 10$
(c) $(2,4,-2)$
$2(2)+(4)-(-2) = 4+4+2 = 10$
The point $(2,4,-2)$ lies in the plane $2x+y-z = 10$
(d) $(-3,6,-10)$
$2(-3)+(6)-(-10) = -6+6+10 = 10$
The point $(-3,6,-10)$ lies in the plane $2x+y-z = 10$
