Question #176337

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


1
Expert's answer
2021-04-11T13:30:31-0400

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:

xx1x2x1=yy1y2y1=zz1z2z1,\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}=\frac{z-z_1}{z_2-z_1},

y23=z13,\frac{y-2}{-3}=\frac{z-1}{-3}, x1=0x-1=0

put coordinates of the third point in the equation

1323\frac{-1}{-3}\not=\frac{2}{-3}

Answer:

False, the plane passes through the points


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