Question

Reduce the equations of the following planes to intercept form and find the intercepts on the coordinate axes. 

2x − y + z = 5

 

 

Answer 1

 Equation of the given plane is 

\[2x - y + z = 5\]

\[\text{ Dividng both sides by 5, we get } \]

\[\frac{2x}{5} + \frac{- y}{5} + \frac{z}{5} = \frac{5}{5}\]

\[ \Rightarrow \frac{x}{\left( \frac{5}{2} \right)} + \frac{y}{- 5} + \frac{z}{5} = 1 . . . \left( 1 \right)\]

\[\text{ We know that the equation of the plane whose intercepts on the coordianate axes are  a,b  and  c is } \]

\[\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1 . . . \left( 2 \right)\]

\[\text{ Comparing (1) and (2), we get } \]

\[a = \frac{5}{2}; b = - 5; c = 5\]