Find the vector and cartesian equation of the plane passing through the point $(0, 1, - 2)$ and normal to the plane is $^i +^j +^k$

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Solution

Let,
the required plane is passing through $(1, 0 - 2)$ and normal to the plane is $^i +^j +^k$
therefore,
vector equation of the plane is

$(\to r - \to a) . \to N = 0$

$[\to r - (^i + 0^j - 2^k)] . (^i +^j +^k) = 0$

putting $\to r = x^i + y^j + z^k$

$[x^i + y^j + z^k - (^i + 0^j - 2^k)] . (^i +^j +^k) = 0$

$[(x - 1)^i + y^j + (z + 2)^k] . (^i +^j +^k) = 0$

$x - 1 + y + z + 2 = 0$

$x + y + z + 1 = 0$

This is the Cartesian equation of the plane.

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Similar questions

Find the vector and Cartesian equations of the planes.

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

that passes through the point (1,4,6) and the normal to the plane is $^i - 2^j +^k .$

(1, 0, - 2)

^i +^j +^k

Find the vector and Cartesian equation of the planes

(a) that passes through the point (1, 0, −2) and the normal to the plane is .

(b) that passes through the point (1, 4, 6) and the normal vector to the plane is .

^i +^j - 2^k,^i + 2^j +^k, 2^i -^j +^k

^i +^j +^k

(2, 3, 4)

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