Consider triangle AOB ln, the x-y plane ,where A≡(1,0,0),,B≡(0,2,0), and O≡(0,0,0).The new position of O, when triangle is rotated about side AB by 90o can be

Equation of line AB is x−11=y−2=z0=λNow AB⊥OC⇒1(λ+1)+(−2λ)(−2)=05λ=−1 or λ=−15C is 45,25,0. Now x12+y1−22+z12=4----ix1−12+y12+z12=1-----ii Now OC⊥CD⇒ x1−4545+y1−2525+z1−00=0----iiiFrom (i) and (ii), we getFrom (iii), putting x1=2y1⇒2y1=45 or y1=25⇒x1=45 Putting this value of x1, and y1 in (i), we getz1=±25