Three planes are perpendicular to each other. Their three intersecting lines intersect at a point O. the distances from P to the three planes are 3, 4 and 5 respectively. Then the length of OP is

Three planes are perpendicular to each other. Their three intersecting lines intersect at a point O. the distances from P to the three planes are 3, 4 and 5 respectively. Then the length of OP is

In fact, the answer is to find the line connecting the two opposite vertices of a cuboid with three edges equal to 3, 4 and 5, which is equal to the square of 3 + the square of 4 + the square of 5 = 5 times the root sign 2

If the three planes are perpendicular to each other, their three intersecting lines intersect at a point O, and the distances from P to the three planes are 3, 4 and 5 respectively, then the length of OP is______ ．

Construct cuboids with edge lengths of 3, 4 and 5, so that OP is the diagonal of the cuboid. So OP = 32 + 42 + 52 = 52

If the three planes are perpendicular to each other, their three intersecting lines intersect at a point O, and the distances from P to the three planes are 3, 4 and 5 respectively, then the length of OP is______ ．

Construct cuboids with edge lengths of 3, 4 and 5, so that OP is the diagonal of the cuboid. So OP = 32 + 42 + 52 = 52