Prove that if a plane has the intercepts a, b, c and it is at a distance p units
from the origin, then `(1)/a^2 + (1)/b^2+(1)/c^2 = (1)/p^2`

Consider the points A(2,-3,0) and B (-1,1,c) If the distance is 13 units, find the values of c

The line L has intercepts a and b on the coordinate axes. Keeping the origin fixed, the coordinate axes are rotated through a fixed angle. If the line L has intercepts p and q on the rotated axes, then (1)/(a^(2)) + (1)/(b^(2)) is equal to

If p be the measure of the perpendicular segment from the origin on the line whose intercepts on the axis are a and b show that 1/p^2= 1/a^2 + 1/b^2

If' p is the length of perpendicular from the origin to the line whose intercepts on. the axes are a and b , then show that 1/p^2=1/a^2+1/b^2

Suppose that a, b, c are in A.P. Prove that 2b = a + c

If the line (x+1)/(2) = (y+1)/(3) = (z+1)/(4) meets the plane x + 2y + 3z = 14 at P, then the distance between P and the origin is a) sqrt(14) b) sqrt(15) c) sqrt(13) d) sqrt(12)

If the square of the matrix [[a,b],[a,-a]] is the unit matrix, then b is equal to a) (a)/(1+a^(2)) b) (1-a^(2))/(a) c) (1+a^(2))/(a) d) (a)/(1-a^(2))