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Line Lies in a Plane
A line:
$$\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}$$
lies in plane:
$$Ax+By+Cz+D=0$$
if:
$$Aa+Bb+Cc=0$$
and:
$$Ax_1+By_1+Cz_1+D=0$$
Usage
- Used to verify that every point of a line belongs to a given plane.
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Line Lies in a Plane
A line:
$$\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}$$
lies in plane:
$$Ax+By+Cz+D=0$$
if:
$$Aa+Bb+Cc=0$$
and:
$$Ax_1+By_1+Cz_1+D=0$$
Usage
- Used to verify that every point of a line belongs to a given plane.
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