A plane passing through (-1, 2, 3) and whose | vedclass

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(C) The equation of a plane passing through the point $(x_0, y_0, z_0) = (-1, 2, 3)$ is given by $a(x - x_0) + b(y - y_0) + c(z - z_0) = 0$,where $\la

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$x+y+z-4=0$

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(C) The equation of a plane passing through the point $(x_0, y_0, z_0) = (-1, 2, 3)$ is given by $a(x - x_0) + b(y - y_0) + c(z - z_0) = 0$,where $\langle a, b, c \rangle$ are the direction ratios of the normal to the plane.Substituting the point,we get $a(x + 1) + b(y - 2) + c(z - 3) = 0$.Since the normal makes equal angles $\alpha$ with the coordinate axes,the direction cosines are $\cos \alpha, \cos \alpha, \cos \alpha$.Thus,the direction ratios $a, b, c$ can be taken as $1, 1, 1$.Substituting these into the equation of the plane:$1(x + 1) + 1(y - 2) + 1(z - 3) = 0$$x + 1 + y - 2 + z - 3 = 0$$x + y + z - 4 = 0$.

$A$ plane passing through $(-1, 2, 3)$ and whose normal makes equal angles with the coordinate axes is

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