JEE Main & Advanced
Mathematics
Three Dimensional Geometry
Question Bank
Critical Thinking
question_answer
A square \[ABCD\] of diagonal 2a is folded along the diagonal \[AC\] so that the planes \[DAC\] and \[BAC\] are at right angle. The shortest distance between \[DC\] and \[AB\] is [Kurukshetra CEE 1998]
A)\[\sqrt{2}a\]
B)\[2a/\sqrt{3}\]
C)\[2a/\sqrt{5}\]
D)[(\sqrt{3}/2)a\]
Correct Answer:
B
Solution :
When folded co-ordinates will be \[D\,(0,\,\,0,\,\,a);\,\,C\,(a,\,0,\,0);\]
\[A(-a,\,\,0,\,\,0);\,\,B\,(0,\,\,-a,\,\,0)\]
Equation \[DC\text{ is, }\frac{x}{a}=\frac{y}{0}=\frac{z-a}{-a}\]