Question

True or false,justify[no plane passes through the points(1,2,3),(1,-1,0)and(1,1,2)].

Answer 1

In a three-dimensional space, a plane can be defined by three points it contains, as long as those points are not on the same line.

Find the equation of a line use first and second points:

$\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}=\frac{z-z_1}{z_2-z_1},$

$\frac{y-2}{-3}=\frac{z-1}{-3},$ $x-1=0$

put coordinates of the third point in the equation

$\frac{-1}{-3}\not=\frac{2}{-3}$

Answer:

False, the plane passes through the points