Can the direction cosines of a line be `1/sqrt2 , 1/sqrt2, 1/sqrt2`?

1/sqrt2 is

If the direction cosines of a line are 1/sqrt(3), 1/(2sqrt(2)), k , then the value of 48k=

If the direction cosines of two lines are (1)/(sqrt(6)),(-1)/(sqrt(6)),(2)/(sqrt(6))and(2)/(sqrt(6)),(1)/(sqrt(6)),(-1)/(sqrt(6)) respectively, then the acute angle between them is

Find the angle between the plane x+y-2z+5=0 and the line whose direction cosines are 1/sqrt(6),2/sqrt(6),1/sqrt(6) .

A straight line L on the xy-plane bisects the angle between OX and OY. What are the direction cosines of L? a.(:(1/sqrt(2)),(1/sqrt(2)),0:)b(:(1/2),(sqrt(3)/2),0:)c.(:0,0,1:)d(:(2/3),(2/3),(1/3):)

If the direction ratios of a line are proportional to 1, -3, 2 then its direction cosines are 1/(sqrt(14)),-3/(sqrt(14)),2/(sqrt(14)) b. 1/(sqrt(14)),2/(sqrt(14)),3/(sqrt(14)) c. -1/(sqrt(14)),3/(sqrt(14)),2/(sqrt(14)) d. -1/(sqrt(14)),-2/(sqrt(14)),-3/(sqrt(14))

If (1)/(sqrt(2)),(1)/(2) , n are the direction consines of a line, then n =

1/(1+ sqrt2 + sqrt3)

The angle between the two lines having direction cosines (2/sqrt(6),-1/sqrt6,1/sqrt6) and (1/sqrt6,1/sqrt6,2/sqrt6) is