JEE Advanced Model Paper 8 with solutions for online practice

Let the rectangle ABCD initially lies in xy plane with B lying at origin BC along x-axis and BAalong y-axis.
Equation of BD in xy-plane is y = 2x
So, the coordinates of foot N of C on BD are (

r

2

,

2r

5

) and length CN =

2r

√3

Clearly , CN = C1N
Hence, the coordinates of various points in 3-D are
A (0 , 2r , 0) , C (r , 0 , 0) , D (r , 2r , 0) , N (

r

5

,

2r

5

,0) and C1 (

r

5

,

2r

5

,

2r

√5

)
Now , AC1 =

√85r

5

Direction cosines of BC1 =

1

5

,

2

5

,

2

√5

⇒ cos θ =

2

5

Any point on AB (x1,y1,z1) = (0 , 0 , 0)
Any point on CD1 (x2,y2,z2) = (r , 2r , 0)
Direction cosines of AB = 0 , 1 , 0 = I1,m1,n1
Direction cosines of C1D =

2

5

,

4

5

,−

1

√5

= I2,m2,n2
Desired shortest distance =
= units