Question

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

Options

•  x + y + z = 1

•  x + y + z = 0

• x + y − z = 1

•  x + y + z = 2

   

Answer 1

 x + y + z = 1

 

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