Determine whether the points are coplanar. (1,2,7),(-3,6,6),(4,4,2),(3,3,4)

Name: Problem 50, Chapter 3: Elementary Linear Algebra
Uploaded: 2022-02-19T17:24:58-08:00
Duration: 3 min 9 s
Channel: Haricharan Gupta
Description: Determine whether the points are coplanar. (1,2,7),(-3,6,6),(4,4,2),(3,3,4)

step 1 Hello students we are given that we need to check those points are co -planner or not okay First

Determine whether the points are coplanar....

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Key Concepts

Coplanarity

Coplanarity refers to the property of a set of points lying within the same geometric plane. In three-dimensional space, detecting coplanarity often involves checking if the vectors formed by the points satisfy a specific condition that indicates they all lie within a single plane.

Vector Subtraction

Vector subtraction is used to create direction vectors from the given points. By subtracting the coordinates of one point from another, vectors that lie along the plane can be formed, which then serve as the basis for further analysis like checking for coplanarity.

Scalar Triple Product

The scalar triple product is a method to compute the volume of a parallelepiped defined by three vectors. In the context of coplanarity, if the scalar triple product of three vectors is zero, it indicates that the volume is zero, meaning the vectors (and thus the points from which they are derived) are coplanar.

Determinant

The determinant of a 3x3 matrix, formed by the coordinates of vectors, is used in the calculation of the scalar triple product. A zero determinant signifies that the vectors are linearly dependent, which is equivalent to stating that the points lie on the same plane.

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