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Question

If α+β+γ=aδ and β+γ+δ=bα,α and δ are non-collinear, then α+β+γ+δ equals

A
aα
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B
aδ
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C
0
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D
(a+b)+γ
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Solution

The correct option is C 0
Given α+β+γ=aδ ............................................................(i)
β+γ+δ=bα ...................................................................(ii)
From (i), α+β+γ+δ=(a+1)δ... .......................................................(iii)
From (ii), α+β+γ+δ=(a+1)α ........................................................(iv)
From (iii) and (iv), we get,
(a+1)δ=(b+1)α .........................................(v)
Since α is not parallel to δ,
From (v), a+1=0 and b+1=0
From (iii), α+β+γ+δ=0

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