A line makes angles α,β,γ,δ with the diagonals of a cube. Then ∑cos2α=1λwhere λ=

let l be the line having directions cosines l,m,ndiagonals of cube are OP,CS,BQ,ARdirection ratios OP  are 1,1,1direction ratios CS  are 1,1,-1direction ratios BQ are 1,-1,1direction ratios AR  are -1,1,1Given  α,β,γ,δ  are angles made by the  line with diagonalscosα=l1+m1+n1l2+m2+n212+12+12           =l+m+n3cosβ=l+m+n3,cosγ=l-m+n3,cosδ=-l+m+n3cos2α+cos2β+cos2γ+cos2δ=l+m+n23+l+m−n23+l−m+n23+−l+m+n23=13+13+13+13=43