Paragraph: Let L : x+y+z+4=0=2 x-y-z+8 be a line and P : x+2 y+3 z+1=0 be a plane Question: What are the direction ratios of the line?

Step-by-step solution

We have L : x + y + z +4=0=2 x - y - z -8 and P: x+2 y+3 z+1=0 is a plane. Let Dr's of line a, b, c Since, line L obtained by intersection of planes x+y+z+4=0 and 2 x-y-z-8=0 So, a + b + c =0 .....(i) 2 a-b-c=0 ....(ii) (line is perpendicular to normal of both plane) aligned & a -1+1 = b 2+1 = c -1-2 = & a =0, ~b =3 , c =-3 aligned (solving (i) and (ii) Dr's of line is 0,3,-3 or 0,1,-1