A plane P passes through the line of intersection of the planes 2 x - y +3 z =2, x + y - z =1 and the point (1,0,1) . What are the direction ratios of the line of intersection of the given planes?

Step-by-step solution

To find, intersection point first put z=0 aligned & 2 x-y=2 & x+y=1 & 3 x=3 & x=1 & x+y=1 & y=1-x aligned At x=1, y=0(x, y, z) (1,0,0) Putting x=0 aligned & y-z=1 & -y+3 z=2 2 z=3 & z= 3 2 & y=1+z=1+ 3 2 = 5 2 & (x, y, z) (0, 5 2 , 3 2 ) aligned Point of intersection (x₁, y₁, z₁ ) (1,0,0) (x₂, y₂, z₂ ) (0, 5 2 , 3 2 ) Hence direction ratios of the line of intersection of given plane 2,-5,-3 .