The equation of the plane which cuts equal intercepts of unit length on the coordinate axes is
(a) x + y + z = 1
(b) x + y + z = 0
(c) x + y − z = 1
(d) x + y + z = 2

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Solution

(a) x + y + z = 1

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

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The equation of the plane which cuts equal intercepts of unit length on the coordinate axes is (a) x + y + z = 1 (b) x + y + z = 0 (c) x + y − z = 1 (d) x + y + z = 2

The equation of the plane which cuts equal intercepts of unit length on the coordinate axes is
(a) x + y + z = 1
(b) x + y + z = 0
(c) x + y − z = 1
(d) x + y + z = 2