Show that if `x^2+y^2=1`, then the point `(x,y,sqrt(1-x^2-y^2))` is at a distance of 1 unit from the origin.

Write the distance of the 2x+y+2z+1=0 from the origin.

Write the distance of the plane 2x-y+2z+1=0 from the origin.

Find the points on the line (x+2)/3=(y+1)/2=(z-3)/2 at a distance of 5 units from the point (1,3,3).

Find the equation of the plane containing the lines 2x-y+z-3=0, 3x+y+z=5 and at a distance of 1/sqrt6 from the point (2,1,-1) .

The equation of the plane passing through the line of intersection of the planes x+2y+3z=2 and x-y+z=3 at a distance 2/sqrt3 from the point (3,1,-1) is :

Find the equation of the planes parallel to the plane x-2y+2z-3=0 and which is at a unit distance from the point A(1,1,1) .

The coordinates of a point on the line (x-1)/(2)=(y+1)/(-3)=z at a distance 4sqrt(14) from the point (1, -1, 0) are

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.

Show that the function ,y, defined by y(x) = sqrt(1+x^(2)) (x in R) is the solution of (1+x^(2))y' = xy

What is the distance of the point (-1,2,1) from the plane 2x-3y+4z+5=0.