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The number of planes passing through three non-collinear points is always [[1]].

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Detailed Solution

The number of planes passing through three non-collinear points is always 1.
Suppose the three non-collinear points are,

(x 1, y 1, z 1), (x 2, y 2, z 2), (x 3, y 3, z 3)

One plane will be formed using the tree points.
The equation of the plane passing through the three points will be formed as,

x − x 1 y − y 1 z − z 1 x 2 − x 1 y 2 − y 1 z 2 − z 1 x 3 − x 1 y 3 − y 1 z 3 − z 1 = 0

From here, we can see that only one equation of the plane is possible when we will calculate the determinant of the above matrix.
Therefore, the planes passing through the three non collinear points is always 1.

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