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प्रश्न
Reduce the equations of the following planes to intercept form and find the intercepts on the coordinate axes.
2x − y + z = 5
उत्तर
Equation of the given plane is
\[2x - y + z = 5\]
\[\text{ Dividng both sides by 5, we get } \]
\[\frac{2x}{5} + \frac{- y}{5} + \frac{z}{5} = \frac{5}{5}\]
\[ \Rightarrow \frac{x}{\left( \frac{5}{2} \right)} + \frac{y}{- 5} + \frac{z}{5} = 1 . . . \left( 1 \right)\]
\[\text{ We know that the equation of the plane whose intercepts on the coordianate axes are a,b and c is } \]
\[\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1 . . . \left( 2 \right)\]
\[\text{ Comparing (1) and (2), we get } \]
\[a = \frac{5}{2}; b = - 5; c = 5\]
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