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If for some  αand βin R, the intersection of the following three planes

x+4y-2z=1

x+7y-5z=β

x+5y+α z=5

 is a line in R3, then α+β is equal to: 

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a
0
b
10
c
2
d
-10

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detailed solution

Correct option is B

Given 3 planes has line of intersection which means infinite solutions So, Δ=0⇒14-217-515α=0⇒(7α+25)-(4α+10)+(-20+14)=0⇒α=-3 Also Dz=0⇒14117β155=0⇒1(35-5β)-(15)+1(4β-7)=0⇒β=13α+β=-3+13=10


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