Let L be the line with parametric equations x 6t y 8t z 8

Let L be the line with parametric equations

x = 6t
y = 8+t
z = 8+3t

Find the vector equation for a line that passes through the point P=(10, 5, 10) and intersects L at a point that is distance 3 from the point Q=(6, 8, 8). Note that there are two possible correct answers. Use the square root symbol \'\' where needed to give an exact value for your answer.

Solution

a(x x0) + b(y y0) + c(z z0) =d .
6(x+10) -8(y+5) +8(z-10) = d

6x+60 -8y -40 +8z -80 =3

6x -8y +8z = 57