Introduction to Three Dimensional Geometry

4

6

8

2

(0, y, 0)

(x, 0, 0)

(0, 0, z)

(x, y, 0)

(1, 1, 1)

(0, 1, 0)

(0, 0, 0)

(1, 0, 0)

Second octant

Fourth octant

Sixth octant

Eighth octant

5

$\sqrt{12}$

$5\sqrt{2}$

50

$2\sqrt{14}$

$\sqrt{14}$

$14$

$4\sqrt{7}$

$\left(\frac{mx_2 - nx_1}{m-n}, \frac{my_2 - ny_1}{m-n}, \frac{mz_2 - nz_1}{m-n}\right)$

$\left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}, \frac{mz_2 + nz_1}{m+n}\right)$

$\left(\frac{mx_2 + nx_1}{2}, \frac{my_2 + ny_1}{2}, \frac{mz_2 + nz_1}{2}\right)$

$\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2}\right)$

(3, 2, 1)

(1, 1, 3)

(6, 4, 2)

(3, 1, 2)

$\left(\frac{x_1+x_2+x_3}{2}, \frac{y_1+y_2+y_3}{2}, \frac{z_1+z_2+z_3}{2}\right)$

$\left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}, \frac{z_1+z_2+z_3}{3}\right)$

$(x_1+x_2+x_3, y_1+y_2+y_3, z_1+z_2+z_3)$

$\left(\frac{x_1x_2x_3}{3}, \frac{y_1y_2y_3}{3}, \frac{z_1z_2z_3}{3}\right)$

$x = 0$

$y = 0$

$z = 0$

$x + y + z = 0$