Question
Sun January 06, 2013 By: Akhil Mohan
 

A straight line passing through (1,1,1)makes an angle 60 with the positive direction of z-axis and cosines of the angle made with the positive direction of y-axis and x-axis are in the ratio sq.root 3: 1.then the acute angle between the two possible position of the line is ? plz help with this problem with method

Expert Reply
Sun January 06, 2013
as
 cos^2(a)+cos^2(b)+cos^2(c)=1
 here cosa=1/2
cos b=sq root3 *p
cosc=1p
here p is a constant
1/4+3p^2+p^2=1
4p^2=3/4
p=root3/4
or p=-root3/4
angle between two lines
           lines will be=
r1=t(1/2i+3/4j+root3/4k)
r2=s(1/2i-3/4j-root3/4k)
angle between two lines cosQ=1/4-9/16-3/16
                                         =-1/2
                                       Q=120 degree
 
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