A) \[a=8,b=2\]
B) \[a=2,b=8\]
C) \[a=4,b=6\]
D) \[a=6,b=4\]
Correct Answer: D
Solution :
[d]: The equation of the line passing through (3, b, 1) and (5,1, a) is \[\frac{x-5}{2}=\frac{y-1}{1-b}=\frac{z-a}{a-1}=\mu (say)\] The line crosses the yz plane where x = 0, i.e., \[-5=2\mu \therefore \mu =-\frac{5}{2}\] Again, \[y=\mu (1-b)+1=\frac{17}{2}\] \[\Rightarrow \]\[-\frac{5}{2}(1-b)+1=\frac{17}{2}\] \[\Rightarrow \]\[-\frac{5}{2}(1-b)=\frac{15}{2}\Rightarrow (1-b)=-3\therefore b=4\] Again, \[z=\mu (a-1)+a=-\frac{13}{2}\] \[\Rightarrow \]\[-\frac{5}{2}(a-1)+a=-\frac{13}{2}\Rightarrow -\frac{3}{2}a+\frac{5}{2}=-\frac{13}{2}\] \[\Rightarrow \]\[-\frac{3}{2}a=-9\Rightarrow a=6\]
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