If a line makes acute angles α,β,γ with the coordinate axes such that $$cos$$α$$cos$$β$$=16$$; $$cos$$β$$cos$$γ$$=123$$; $$cos$$γ$$cos$$α$$=132then$$ , $$3cos$$α$$+$$$$cos$$β$$+$$$$cos$$γ$$2=2+3+6+$$λ then λ$$=$$

Question

If a line makes acute angles α,β,γ with the coordinate axes such that $$cos$$α$$cos$$β$$=16$$;  $$cos$$β$$cos$$γ$$=123$$;  $$cos$$γ$$cos$$α$$=132then$$ , $$3cos$$α$$+$$$$cos$$β$$+$$$$cos$$γ$$2=2+3+6+$$λ then λ$$=$$

Infinity Learn · Accepted Answer

If  α,β,γare the angles made by a line with axes then $$cos2$$α$$+cos2$$β$$+cos2$$γ$$=1Consider$$,   $$3cos$$α$$+$$$$cos$$β$$+$$$$cos$$γ$$2$$             $$=3cos2$$α$$+cos2$$β$$+cos2$$γ$$+2cos$$α$$cos$$β$$+2cos$$β$$cos$$γ$$+2cos$$γ$$cos$$α$$=31+26+223+232=3+6+3+2Therefore$$,  λ$$=3$$⇒λ$$=9$$

If a line makes acute angles $α, β, γ$ with the coordinate axes such that $\cos α \cos β = \frac{1}{\sqrt{6}}; \cos β \cos γ = \frac{1}{2 \sqrt{3}}; \cos γ \cos α = \frac{1}{3 \sqrt{2}}$ then , $3 {(\cos α + \cos β + \cos γ)}^{2} = \sqrt{2} + \sqrt{3} + \sqrt{6} + \sqrt{λ}$ then $λ =$

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If a line makes acute angles α,β,γ with the coordinate axes such that cosαcosβ=16; cosβcosγ=123; cosγcosα=132then , 3cosα+cosβ+cosγ2=2+3+6+λ then λ=

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Ready to Test Your Skills?

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If a line makes acute angles $α, β, γ$ with the coordinate axes such that $\cos α \cos β = \frac{1}{\sqrt{6}}; \cos β \cos γ = \frac{1}{2 \sqrt{3}}; \cos γ \cos α = \frac{1}{3 \sqrt{2}}$ then , $3 {(\cos α + \cos β + \cos γ)}^{2} = \sqrt{2} + \sqrt{3} + \sqrt{6} + \sqrt{λ}$ then $λ =$