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Question

If for some α and β in R, the intersection of the following three planes
x+4y2z=1x+7y5z=βx+5y+αz=5
is a line in R3, then α+β is equal to :

A
0
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B
10
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C
10
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D
2
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Solution

The correct option is B 10
The given planes intersect in a line
D=Dx=Dy=Dz=0
D=0
∣ ∣14217515α∣ ∣=0
7α+254α20+4=0α=3

Dz=0
∣ ∣14117β155∣ ∣=0
355β20+4β2=0β=13α+β=10

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