VECTOR ALGEBRA | LINEAR COMBINATION LINEAR INDEPENDENCE AND LINEAR DEPENDENCE | Definition and physical interpretation: Linear Combination, Linear Combination: Linear Independence And Linear Dependence, Linearly Independent, Linearly Dependent, Theorem 1: If `veca` and `vecb` are two non collinear vectors; then every vector `vecr` coplanar with `veca` and `vecb` can be expressed in one and only one way as a linear combination: x`veca`+y`vecb`., Theorem 2: If `veca`, `vecb` and `vecc` are non coplanar vectors; then any vector `vecr` can be expressed as linear combination: x`veca`+y`vecb`+z`vecc`, Theorem 3:If vectors `veca`, `vecb` and `vecc` are coplanar then det(`veca` `vecb` `vecc`) = 0, Examples: Prove that the segment joining the middle points of two non parallel sides of a trapezium is parallel to the parallel sides and half of their sum., Components of a vector in terms of coordinates of its end points