A line makes angles α,β,γ,δ with the diagonals of a cube. Then ∑$$cos2$$α$$=1$$λwhere λ$$=$$

Question

A line makes angles α,β,γ,δ with the diagonals of a cube. Then ∑$$cos2$$α$$=1$$λwhere λ$$=$$

Infinity Learn · Accepted Answer

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$$=l1+m1+n1l2+m2+n212+12+12$$           $$=l+m+n3cos$$β$$=l+m+n3$$,$$cos$$γ$$=l-m+n3$$,$$cos$$δ$$=-l+m+n3cos2$$α$$+cos2$$β$$+cos2$$γ$$+cos2$$δ$$=l+m+n23+l+m$$−$$n23+l$$−$$m+n23+$$−$$l+m+n23=13+13+13+13=43$$

A line makes angles $α, β, γ, δ$ with the diagonals of a cube. Then $\sum \cos^{2} α = \frac{1}{λ}$ where $λ$ =

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

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A line makes angles $α, β, γ, δ$ with the diagonals of a cube. Then $\sum \cos^{2} α = \frac{1}{λ}$ where $λ$ =