How do you find the coordinates of three points P,Q, and R given 4x- 3y -6z = 6?

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Answer 1 · 2017-07-26T17:46:22

This way is easy:

$P = (\frac{3}{2}, 0, 0)$ $P = (3/2,0,0)$ , $Q = (0, - 2, 0)$ $Q = (0,-2,0)$ , and $R = (0, 0, - 1)$ $R = (0,0,-1)$

Let P be of the form $(x, 0, 0)$ $(x,0,0)$ :

$4 x - 3 (0) - 6 (0) = 6$ $4x-3(0)-6(0) = 6$

$x = \frac{6}{4}$ $x = 6/4$

$x = \frac{3}{2}$ $x = 3/2$

$P = (\frac{3}{2}, 0, 0)$ $P = (3/2,0,0)$

Let Q be of the form $(0, y, 0)$ $(0,y,0)$

$4 (0) - 3 (y) - 6 (0) = 6$ $4(0)-3(y)-6(0) = 6$

$- 3 y = 6$ $-3y = 6$

$y = - 2$ $y = -2$

$Q = (0, - 2, 0)$ $Q = (0,-2,0)$

Let R be of the form $(0, 0, z)$ $(0,0,z)$

$4 (0) - 3 (0) - 6 (z) = 6$ $4(0)-3(0)-6(z) = 6$

$- 6 z = 6$ $-6z = 6$

$z = - 1$ $z = -1$

$R = (0, 0, - 1)$ $R = (0,0,-1)$