The point P is the intersection of the straight line joining the points `Q(2, 3, 5)` and `R (1, -1, 4)` with the plane `5x- 4y-z=1`. If S is the foot of the perpendicular drawn from the point `T(2, 1, 4)` to QR, then the length of the line segment PS is:

The point P is the intersection of the straight line joining the point

1.	The point P is the intersection of the straight line joining the points `Q(2, 3, 5)` and `R (1, -1, 4)` with the plane `5x- 4y-z=1`. If S is the foot of the perpendicular drawn from the point `T(2, 1, 4)` to QR, then the length of the line segment PS is:
Answer» `L:(x-1)/1=(y+1)/4=(z-4)/1=lambda` `(lambda+1,4lambda-1,lambda+4)` `5x-4y-z=1` `5(lambda+1)-4(4lambda-1)-(lambda+4)=1` `-12lambda+5=1` `lambda=1/3` `vec(TS)(lambda-1,4lambda-2,lambda)` `(1,4,1)` `lambda-1+16lambda-8+lambda=0` `lambda=1/2` `P(4/3,1,13/3),S(3/2,1,9/2)` `PS=sqrt((3/2-4/3)^2+(9/2-13/3)^2)` `PS=sqrt(1/6^2+1/6^2)` `PS=sqrt2/6=1/(3sqrt2)`.

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The point P is the intersection of the straight line joining the points `Q(2, 3, 5)` and `R (1, -1, 4)` with the plane `5x- 4y-z=1`. If S is the foot of the perpendicular drawn from the point `T(2, 1, 4)` to QR, then the length of the line segment PS is:

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