Paragraph: A line L passes through the point P (5,-6,7) and is parallel to the planes x + y + z =1 and 2 x - y -2 z =3 . Question: What are the direction ratios of the line of intersection of the given planes?

Step-by-step solution

Let a, b, c be the direction ratios of the line. Then its equation is x-5 a = y+6 b = z-7 c ...(i) Since (i) is parallel to the planes x+y+z=1 and 2 x-y-2 z=3 then a(1)+b(1)+c(1)=0 and a(2)+b(-1)+c(-2)=0 By cross multiplication aligned & a -1 = b 4 = c -3 = & a=- , b=4 , c=-3 aligned Direction ratios of the line are -1,4,-3 = 1,-4,3 Substituting a, b , c in (i), we get x-5 -1 = y+6 4 = z-7 -3 ...(ii) Hence equation of the line is x-5 -1 = y+6 4 = z-7 -3