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# The perpendicular distance of a corner of unit cube from a diagonal not passing through it is ???

Arun
25763 Points
3 years ago
Dear student

The perpendicular distance of a corner of unit cube from a disgonal not passing through it is $\sqrt$(2/3)
Regards
Khimraj
3007 Points
3 years ago
Let the edges Of unit cube are OA along z axis,OB along x axis and OC along y axis.
Let CM be the perpendicular from corner C on diagonal OP where point P is (1,1,1)
OP=i+j+k
OP=|i+j+k|=3
Unit vector in the direction of OP is (i+j+k)/√3
OM= projection of OC on OP
OM= OC.(unit  vector ofOP)
OM=j.((i+j+k)/3)=13
Now CM2=OC2OM2
CM2=11/3 = 2/3
So CM = $\sqrt{2/3}$.