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?`

Statement 1:If the point (2a-5,a^2) is on the same side of the line x+y-3=0 as that of the origin, then a in (2,4) Statement 2: The points (x_1, y_1)a n d(x_2, y_2) lie on the same or opposite sides of the line a x+b y+c=0, as a x_1+b y_1+c and a x_2+b y_2+c have the same or opposite signs.

The range of values of theta in the interval (0, pi) such that the points (3,2) and (sin theta , cos theta) lie on the same side of the line x+y-1=0 , is

then image of the point (-1,3,4) in the plane x-2y=0

If P is a point (x ,y) on the line y=-3x such that P and the point (3, 4) are on the opposite sides of the line 3x-4y=8, then

Find the distance , (i) Between two points (5,4) and (2,0) (ii) From a point (1,2) to the line 5x+12y-3=0 (iii) Between two parallel lines 3x+4y=12 and 6x+8y+1=0

Find the equation of the plane that contains the point (1,-1,2) and is perpendicular to each of the planes 2x+3y-2z=5 and x+2y-3z=8.

Find the vector and Cartesian equations of the plane passing through the point (1,1,-1) and perpendicular to the planes x + 2y + 3z - 7 = 0 and 2x - 3y + 4z = 0

Find the equation of a plane which passes through the point (1,2,3) and which is equally inclined to the planes x-2y+2z-3=0a n d8x-4y+z-7=0.

Find the equation of the plane passing through the point (-1,3,2) and perpendicular to each of the planes x+2y+3z=5 and 3x+3y+z=0.

Find the points on the line x + y = 5 , that lie at a distance 2 units from the line 4x - 3y - 12 = 0 .