How do you tell if four points are coplanar

1 answer:

3 0

You know that three points A,B,CA,B,C (two vectors A⃗ BA→B, A⃗ CA→C) form a plane. If you want to show the fourth one DD is on the same plane, you have to show that it forms, with any of the other point already belonging to the plane, a vector belonging to the plane (for instance A⃗ DA→D).

Since the cross product of two vectors is normal to the plane formed by the two vectors (A⃗ B×A⃗ CA→B×A→C is normal to the plane ABCABC), you just have to prove your last vector A⃗ DA→D is normal to this cross product, hence the triple product that should be equal to 00:

A⃗ D⋅(A⃗ B×AC)=0

You might be interested in

What are the parts of the circle

Oksanka [162]

The parts of a circle are the r<em>adius, diameter, circumference, arc, chord, secant, tangent, sector and segment.</em>

Radius:

The distance from the center to any point on the circle.

Diameter:

The distance across the circle through the center point.

Circumference:

The distance around a circle.

Arc:

arcs in the same circle that have exactly one point in common. measure of arc divided by 360 multiplied by the circumference. the length of an arc. semicircle. an arc that is half of a circle; always measures 180 degrees.

Chord:

a line segment that connects two points of a circle.

Secant:

A secant is a line that intersects a circle in two points.

Tangent:

A tangent is a line that intersects the circle in exactly one point.

Sector:

region bounded by an arc of a circle and the two radii to the arc's endpoints. - A sector is like a "pizza slice" of the circle. It consists of a region bounded by two radii and an arc lying between the radii.

Segment:

A segment or length of a segment with one endpoint at the center of the circle.