The equation of the plane which cuts equal intercepts of unit length on the coordinate axes is

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x + y + z = 1 	ext{ We know that the equation of aplane whose intercepts are a, b, c is } x/a + y/b + z/c = 1 . . . \left( 1 ight) 	ext{ It is given that a = b = c } 	ext{ So, from (1),} x/a + y/a + z/c = 1 \Rightarrow x + y + z = a . . . (2) 	ext{ Since it is given that the intercepts of the required plane are of unit length,} a = b = c = 1 	ext{ Substituting a = 1 in (2), we get } x + y + z = 1

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