Question

Let P be a point not on the line L that passes through the points Q and R. The distance d from the point P to the line L is d = |a × b| |a| where a = QR and b = QP. Use the above formula to find the distance from the point to the given line. (0, 1, 1); x = 2t, y = 5 − 2t, z = 1 + t

Answer 1

Answer:

Distance from point (0,1,1) to the given line is zero.

Step-by-step explanation:

Given parametric equations of line,

x=2t, y=5-2t, z=1+t

To find distance from (0,1,1), we have to eliminate t from above equations so that,

$y=5-2t=5-x\implies x+y=5=4+1=4+z-t=4+z-\frac{1}{2}x$

$\implies 3x+2y-2z-8=0\hfill (1)$

whose direction ratioes are (l,m,n)=(3,2,-2) and distance fro point (a,b,c)=(0,1,1) is given by,

$\frac{al+bm+cn}{\sqrt{l62+m^2+n^2}}=\frac{(3\times 0)+(2\times 1)+(-2)(1)}{\sqrt{3^2+2^2+(-2)^2}}=\frac{0+2-2}{\sqrt{17}}=0$

Distance between point (0,1,1) and (1) is zero. That is point 90,1,1) is lies on the line (1).