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The equation of plane passing through the intersection of planes $x+y-z=2$ and $2x-y+3z=5$ and parallel to the line $p=i+a (2i-j)$ is?

$\text {Attempt }$: We know the equation of such plane is $r_1+b(r_2)=n_1+b (n_2) $ where $r_1,r_2$ are planes and $n_1,n_2$ are constants. Also it is given that its parallel to a line with direction ratios $2,-1,0$ thus the direction ratios of its normal are $1,2,0$ . So this satisfies the equation of third plane which passes through intersection of two planes . So I put values to get $b=1/5$ but I am not getting the right answer as my solution and answer keys' solution is not matching . Where is my fault in understanding the question? Thanks!

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    I think it should be a "minus" sign. Please check my edit. – 2017-01-11
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    Where? I see everything correct – 2017-01-11
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    You wrote the first equation as $x+y_z=3$. – 2017-01-11
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    @SchrodingersCat Ask first, Edit next – 2017-01-11
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    Ya its right. Thanks! – 2017-01-11

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