Find the equation of the plane passing throug | vedclass

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(B) The equation of a plane parallel to $x + y + z = 0$ is of the form $x + y + z + \lambda = 0$,where $\lambda$ is a constant.Since the plane passes

Vedclass · Accepted Answer

$x + y + z = \alpha + \beta + \gamma$

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(B) The equation of a plane parallel to $x + y + z = 0$ is of the form $x + y + z + \lambda = 0$,where $\lambda$ is a constant.Since the plane passes through the point $(\alpha, \beta, \gamma)$,we substitute these coordinates into the equation:$\alpha + \beta + \gamma + \lambda = 0$Solving for $\lambda$,we get $\lambda = -(\alpha + \beta + \gamma)$.Substituting the value of $\lambda$ back into the equation of the plane,we get:$x + y + z - (\alpha + \beta + \gamma) = 0$Rearranging the terms,we get $x + y + z = \alpha + \beta + \gamma$.

Find the equation of the plane passing through the point $(\alpha, \beta, \gamma)$ and parallel to the plane $x + y + z = 0$.

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