For what value (s) of `a` will the two points `(1,a,1) and (-3,0,a)` lie on opposite sides of the plane `3x+4y-12z+13=0?`

For what value (s) of a will the two points (1,a ,1)a n d(-3,0,a) lie on opposite sides of the plane 3x+4y-12 z+13=0? a. a >-1ora >1//3 b. a=0 only c. 0

Are the points (2,1) and (-3,5) on the same or opposite side of the line 3x - 2y + 1 = 0 ?

Show that the points (1, 1, 1) and (-3, 0, 1) are equidistant from the plane 3x+4y-12 z+13=0.

If the points (1, 2) and (3, 4) were to be on the opposite side of the 3x - 5y + alpha = 0 , then:

Assertion: The points (2,1,5) and (3,4,5) lie on opposite side of the plane 2x+2y-2z-1=0 , Reason: Values of 2x+2y-2z-1 for points (2,1,5) and (3,4,3) have opposite signs. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Let L be the line y = 2x , in the two dimensional plane . Statement 1 : The image of the point (0,1) in L is the point (4/5 , 3/5) Statement 2 : The points (0,1) and (4/5 , 3/5) lie on opposite sides of the line L and are at equal distance from it .

Find the equation of the plane throughathe points (2,-3,1) and (5,2,-1) and perpendicular to the plane x-4y+5z+2=0

Find the image of the point O(0,0,0) in the plane 3x+4y-6z+1=0

The equation of the plane which passes through the points (2, 1, -1) and (-1, 3, 4) and perpendicular to the plane x- 2y + 4z = 0 is

Ifthe points (1,1, lambda) and (-3,0,1) are equidistant from the plane, 3x + 4y-12z + 13 = 0 , then lambda satisfiesthe equation