Distance between points

**Apprentice123** · June 24th 2008, 05:06 PM

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)

**o_O** · June 24th 2008, 05:12 PM

$d = \sqrt{(x_{1} - x_{2})^2 +(y_{1} - y_{2})^2 + (z_{1} - z_{2})^2}$

$3 = \sqrt{(x - 0)^2 + ({\color{red}y} - 2)^2 + ({\color{blue}z} - 1)^2}$

$3 = \sqrt{x^2 + ({\color{red}-x + 2} - 2)^2 + ({\color{blue}2x - 2} -1)^2}$

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.

**Apprentice123** · June 24th 2008, 05:14 PM

is obvious. thanks

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