A line having direction ratios ⟨1,0,3⟩cuts  planes x-y+6z=6 and x-y+6z=4 at P and Q then PQ.

Suppose that  θ be the acute angle between the line whose direction ratios are ⟨1,0,3⟩ and the plane x-y+6z=6hence,  sinθ=al+bm+cna2+b2+c2l2+m2+n2=1+181+91+1+36=191038and sinθ=PMPQ where PM is perpendicular distance from the point to the plane, or it is equal to the distance between two parallel planes. hence, PM=c2−c1a2+b2=21+1+36=238Therefore, PQ=PMsinθ=238103819=21019