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Find the acute angle between the planes with equations $$ x-2 y+z-9=0 \quad \text { and } \quad x+y-z+2=0 $$ The planes meet in the line $l$, and $A$ is the point on $/$ whose position vector is $p \mathbf{i}+q \mathbf{j}+\mathbf{k}$.
(i) Find $p$ and $q$.
(ii) Find a vector equation for $l$.

Normally to find the intersecting line 3 planes will be provided but here only 2 planes are given, though i have to find 3 variables. please some one help me to find the equation of line of intersection

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Writhing down the solutions of the system of equations of the two planes gives you directly their intersection line. e.g. if the planes are $x+y+z=0$ and $x-y-2z=1$, then from the first equation $z=-x-y$. Plug it in the second equation gives $x-y-2(-x-y)=1$, that is $3x+y=1$. Hence the solutions set is $$ \ell=\{(t,1-3t,2t-1):t\in R\}=\{(0,1,-1)+t(1,-3,2):t\in R\} $$ so the parametric equation of the line is $$ \ell(t)=(0,1,-1)+t(1,-3,2) $$

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