1.1.43 Vector Algebra
Condition: Prove that if \( \alpha[a, b]+\beta[b, c]+ \) \( +\gamma[c, a]=0 \), and at least one of the numbers \( \alpha, \beta \) and \( \gamma \) is non-zero, then the vectors \( a, b \) and \( c \) coplanar.
Vector algebra is a branch of algebra that studies linear operations on vectors and their geometric properties. In the section you will find problems on the decomposition of vectors, scalar, vector and mixed products, coordinates of vectors in different bases and much more.