13. If a line L is the line of intersection of the planes 2 x+3 y+z=1 and x+3 y+2 z=2 . If line L makes an angle with the positive X -axis, then the value of is

Step-by-step solution

Given equations: aligned & 2 x+3 y+z=1 & 2 x+3 y=1-z ... (i) & x+3 y+2 z=2 & x+3 y=2-2 z ... (ii) aligned Subtracting (ii) from (i), we get aligned & 2 x+3 y-x-3 y=1-z-2+2 z & x=-1+z & z= x+1 1 ... (iii) aligned Putting value of x in equation (ii), we get aligned & -1+z+3 y=2-2 z & 3 z=3-3 y & z= y-1 -1 ... (iv) aligned From (iii), (iv) x+1 1 = y-1 -1 = z 1 Thus, angle between above line and X -axis having Direction Ratio's (1,0,0) is given as aligned & = | 1 (1)+0+0 1+1+1 1 |= 1 3 & = 3 aligned