What does collinear and non collinear vectors mean
google is your friend.
collinear - they lie in the same straight line.
Collinear and non-collinear vectors are terms used to describe the relationship between two or more vectors in a coordinate system.
1. Collinear vectors: Collinear vectors are vectors that lie on the same line or are parallel to each other. In other words, if two or more vectors have the same or parallel directions, they are collinear vectors. Mathematically, given vectors A, B, and C, if A is parallel to B and B is parallel to C, then A, B, and C are collinear vectors.
2. Non-collinear vectors: Non-collinear vectors are vectors that do not lie on the same line and are not parallel to each other. In other words, if two or more vectors have different or non-parallel directions, they are non-collinear vectors.
To determine whether vectors are collinear or non-collinear, you can perform the following steps:
Step 1: Find the direction of each vector. For instance, if vector A is (2, 3, 4), vector B is (-1, -2, -3), and vector C is (-4, -6, -8), you can observe that the direction of vector A is positive along each coordinate axis, the direction of vector B is negative along each coordinate axis, and the direction of vector C is also negative along each coordinate axis.
Step 2: Compare the directions of the vectors. If the directions are identical or parallel, then the vectors are collinear. If the direction of at least one vector differs from the others, the vectors are non-collinear.
It is important to note that collinearity and non-collinearity are based on the relationship between the vectors' directions and not their lengths or magnitudes.