The new definition of conjugate of z ,
is b + ia = i(a − ib) which is i time old definition
Let the rectangle ABCD initially lies in xy plane with B lying at origin BC along xaxisand BA
along y-axis.
Equation of BD in xy-plane is y = 2x
So, the coordinates of foot N of C on BD are
(,) and length CN =
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
(,,0) and
C1 (,,) Now ,
AC1 =
Direction cosines of
BC1 =
,
,
⇒ cos θ =
Any point on AB
(x1,y1,z1) = (0 , 0 , 0)
Any point on
C1D (
x2,y2,z2) = (r , 2r , 0)
Direction cosines of AB = 0 , 1 , 0 =
I1 ,
m1,n1 Direction cosines of
C1D=,,− =
I2,m2,n2 Desired shortest distance =
=
=
units