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The vector is a normal vector to the plane, that is to say, perpendicular to the plane.

If P(x0, y0, z0) is a point on the plane, the vector is perpendicular to vector , and its dot product is zero.

Therefore, the equation of the plane can be determined from a point and a normal vector.

Examples

1.Find the equation of the line r, that passes through the point (1, 0, 0) and is perpendicular to the plane x − y − z + 2 = 0.

     A = (1, 0, 0).

2.Find the equation of the plane, π, that passes through the point (1, 1, 1) and is perpendicular to the lines x = λ, y = 0, z = λ.

As the plane and the line are perpendicular, the direction vector of the line is a normal vector of the plane.

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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