- #1
yourmom98
- 42
- 0
how do i prove vectors u v w are coplanar if and only if they are linearly dependent ? i have no idea where to start.
Coplanar vectors are vectors that lie on the same plane. This means that they can be drawn on a flat surface without intersecting each other.
To determine if two vectors are coplanar, you can use the cross product. If the cross product of the two vectors is equal to zero, then they are coplanar.
Linear dependence refers to a situation where one vector can be expressed as a linear combination of other vectors. In other words, one vector can be written as a sum of multiples of other vectors.
To test for linear dependence, you can use the determinant method. If the determinant of the matrix formed by the vectors is equal to zero, then the vectors are linearly dependent. Another method is to use Gaussian elimination to see if one vector can be expressed as a linear combination of the others.
Coplanar vectors and linear dependence are important concepts in science because they help us understand the relationships between different quantities and how they can affect each other. They are also used in various fields such as physics, engineering, and mathematics to solve problems and make predictions.