Find the vector and cartesian equations of the planes that passes through the point $(1, 0, - 2)$ and the normal to the plane is $^i +^j +^k$ .

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Solution

Cartesian equation $(x - 1) (1) + (y - 0) (1) + (z + 2) (1) = 0$
$x - 1 + y + z + 2 = 0$
$x + y + z + 1 = 0$
Vector equation $\to \to z . (^i +^j +^k) + 1 = 0$

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