what is the distance between the z-intercept from the x0intercept in the equation ax+by+cz+d=0.

• z-intercept, z2= -d/c, x2=0, y2=0
  & x-intercept, x1= -d/a, y1=0, z1=0
  distance between z and x, D = [(x2-x1)^2+(y2-y1)^2+(z2-z1)^2)]^1/2
  = [(d/a)^2+(-d/c)^2]^1/2
  = d/ac[a^2+c^2]^1/2
• 13 years agoHelpfull: Yes(25) No(6)
• ax + by + cz + d = 0
  At the z-intercept, 'x' and 'y' are both zero.
  cz + d = 0 --> z = -d/c --> The z-intercept is the point (0, 0, -d/c).
  At the x-intercept, 'y' and 'z' are zero.
  ax + d = 0 --> x = -d/a --> The x-intercept is the point (-d/a, 0, 0).
  The distance between the points (0, 0, -d/c) and (-d/a, 0, 0) is
  sqrt[ (-d/a)2 + (-d/c)2 ] = sqrt (d2/a2 + d2/c2) = d sqrt(1/a2 + 1/c2)
  
  
• 12 years agoHelpfull: Yes(11) No(1)