If the three planes are perpendicular to each other, their three intersecting lines intersect at point O, and the distances from a point P in space to the three intersecting lines are 2,5 ^ (1 / 2) and 7 ^ (1 / 2), respectively, then the length of OP is

If the three planes are perpendicular to each other, their three intersecting lines intersect at point O, and the distances from a point P in space to the three intersecting lines are 2,5 ^ (1 / 2) and 7 ^ (1 / 2), respectively, then the length of OP is

In fact, this problem is to find the distance from a point P to the origin of the coordinate in three-dimensional space. Therefore, Op = root sign (2 ^ 2 + 5 ^ (1 / 2) ^ 2 + 7 ^ (1 / 2) ^ 2) = root sign (4 + 5 + 7) = 4; therefore, the length of OP is 4

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