A line with positive direction cosines passes through the point P (2,-1,2) and makes equal angles with co-ordinate axes. The line meets the plane 2 x+y+z=9 at point Q . Then the length of the line segment PQ equals

Step-by-step solution

Since direction cosines of PQ are equal and positive. The d.r.s. of PQ are 1 3 , 1 3 , 1 3 The equation of the line PQ is aligned & x-2 1 3 = y+1 1 3 = z-2 1 3 & x-2=y+1=z-2= k , say aligned Co-ordinates of the point Q are (k+2, k-1 ; k+2) The point Q lies on the plane 2 x+y+z=9 array ll & 2(k+2)+k-1+k+2=9 & 4 k+5=9 k=1 & Q (3,0,3) & P Q= (3-2)^2+(0+1)^2+(3-2)^2 & = 1+1+1 & = 3 units array