Find the intercepts cut off by the plane 2x + y – z = 5.

Solution

The equation of plane is 2x + y – z = 5
or $fraction numerator 2 straight x over denominator 5 end fraction plus straight y over 5 minus straight z over 5 space equals space 1 space space space space space space space space space or space space space space space fraction numerator straight x over denominator begin display style 5 over 2 end style end fraction plus straight y over 5 plus fraction numerator straight z over denominator negative 5 end fraction space equals space 1$
which is of intercept form $straight x over straight a plus straight y over straight b plus straight z over straight c space equals space 1$ where $straight a equals 5 over 2 comma space space straight b space equals space 5 comma space space straight c space equals space minus 5.$

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Three Dimensional Geometry

Find the intercepts cut off by the plane 2x + y – z = 5.

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