A plane $\pi$ passing through the point $3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ is parallel to the plane which passes through the point $\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$ and perpendicular to the vector $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$. Then, the cartesian equation of $\pi$ is

Let the direction cosines of two lines satisfy the equations $3 l+2 m+n=0$ and $2 m n-3 n l+5 l m=0$. If $\theta$ is the angle between these two lines, then $\cos \theta=$

$(1,-2,1)$ is a point on a plane $\pi$ and $\pi$ is parallel to the plane $x-y-z=0$. If the equation of $\pi$ is $a x+b y+c z-2=0$, then $b-2 c=$

If $M$ is the foot of the perpendicular drawn from $P($ -1,2,-1 ) to the plane passing through the point $A(3,-2,1)$ and perpendicular to the vector $4 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}$, then the length of $P M$ is