A square ABCD is of diagonal 2 a is folded along the diagonal AC so that plane DAC , BAC are at right angles then the shortest distance between DC and AB

Question

A square ABCD is of diagonal 2 a is folded along the diagonal AC so that plane DAC , BAC are at right angles then the shortest distance between DC and AB (A) √2 a (B) a (C) (2 a /√3) (D) √3 a

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/5924bdb9d0e92219bbce28a79c66760e-.png" /> Let O be the centre of square O A, O B, O D along x, y, z axes respectively ⇒ A =( a , 0,0), B =(0, a , 0), D =(0,0, a ) C ≡(- a , 0,0) equation of AB are ( x - a / a )=( y -0/- a )=( z -0/0) and equation of DC are (x-0/a)=(y-0/0)=(z-a/a) Hence,SD =(2 a /√3)

Q. A square $A BC D$ is of diagonal $2 a$ is folded along the diagonal $A C$ so that plane $D A C, B A C$ are at right angles then the shortest distance between $D C$ and $A B$

$2 a$

a

$\frac{2 a}{3}$

$3 a$

Q. A square ABCD is of diagonal 2a is folded along the diagonal AC so that plane DAC,BAC are at right angles then the shortest distance between DC and AB

2​a

a

3​2a​

3​a

Let O be the centre of square & OA,OB,OD along x,y,z axes respectively ⇒A=(a,0,0),B=(0,a,0), D=(0,0,a)&C≡(−a,0,0) equation of AB are ax−a​=−ay−0​=0z−0​ and equation of DC are ax−0​=0y−0​=az−a​ Hence,SD=3​2a​

Q. A square $A BC D$ is of diagonal $2 a$ is folded along the diagonal $A C$ so that plane $D A C, B A C$ are at right angles then the shortest distance between $D C$ and $A B$

$2 a$

$\frac{2 a}{3}$

$3 a$