1.1.49 Vector Algebra
condition: Find at least one value of the parameter \( p \), for which the sequence of vectors \( \bar{a}_{1}=(-1,-1,3), \bar{a}_{2}=(1,2,1), \bar{a}_{3}=(p, p,-2) \) is the basis of the space \( \mathbb{R}^{3} \). b) Find the orthonormal basis of the subspace \( L\left(\bar{a}_{1}, \bar{a}_{2}\right) \), generated by the vectors \( \bar{a}_{1}=(1,-1,2), \bar{a}_{2}=(2,1,0)\).
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.