The Cartesian equation of a plane which passe | vedclass

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(A) Let the intercepts on the coordinate axes be $a, b, c$. Since the intercepts are equal and non-zero,we have $a=b=c$.The intercept form of the equa

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$x+y+z=6$

Vedclass · Answer

(A) Let the intercepts on the coordinate axes be $a, b, c$. Since the intercepts are equal and non-zero,we have $a=b=c$.The intercept form of the equation of a plane is $\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1$.Substituting $a=b=c$,we get $\frac{x}{a} + \frac{y}{a} + \frac{z}{a} = 1$,which simplifies to $x+y+z=a$.Since the plane passes through the point $(2, 2, 2)$,we substitute these coordinates into the equation:$2+2+2 = a \Rightarrow a=6$.Therefore,the required Cartesian equation of the plane is $x+y+z=6$.

The Cartesian equation of a plane which passes through the points $A(2,2,2)$ and makes equal non-zero intercepts on the coordinate axes is

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