# If the equation of a Plane P, passing through the intersection of the planes, $x -4y -z+7=0$and $3x +y+5z=8$ is $ax +by +6z=15$ for some $a, b\epsilon R$, then the distance of the point (3,2-1) from the plane P is________ Option: 1 6 Option: 2 9 Option: 3 3 Option: 4 12

\begin{aligned} &\mathrm{D}_{1}=\left|\begin{array}{ccc} -7 & 4 & -1 \\ 8 & 1 & 5 \\ 15 & \mathrm{~b} & 6 \end{array}\right|=0 \Rightarrow \mathrm{b}=-3\\ &\mathrm{D}=\left|\begin{array}{ccc} 1 & 4 & -1 \\ 3 & 1 & 5 \\ \mathrm{a} & \mathrm{b} & 6 \end{array}\right|=0 \Rightarrow 21 \mathrm{a}-8 \mathrm{~b}-66=0\\ &P: 2 x-3 y+6 z=15\\ &\text { so required distance }=\frac{21}{7}=3 \end{aligned}

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