find the points of (r) that distam 3 units from point A (0,2,1)
(r):
y=-x+2
z=2x-2
Answer:
(2,0,2) and (0,2,-2)
$\displaystyle d = \sqrt{(x_{1} - x_{2})^2 +(y_{1} - y_{2})^2 + (z_{1} - z_{2})^2}$
$\displaystyle 3 = \sqrt{(x - 0)^2 + ({\color{red}y} - 2)^2 + ({\color{blue}z} - 1)^2}$
$\displaystyle 3 = \sqrt{x^2 + ({\color{red}-x + 2} - 2)^2 + ({\color{blue}2x - 2} -1)^2}$
etc. etc.
Solve for x (you'll get two values as you end up solving a quadratic) and plug this into your expressions of y and z.