1.1.51 Vector Algebra

Condition: Given vectors \( \bar{a}=(1,1,-2), \quad \bar{b}=(1,4,1) \), \( \bar{c}=(2,-1,3) \) a) show that \( \bar{a}, \bar{b}, \bar{c}- \) basis of the space \( V^{3} \); b) find the coordinates of the vector \( \bar{d}=(-2,7,-7) \) in the basis \( \bar{a}, \bar{b}, \bar{c} \); c) find the cosine of the angle between the vectors \( \bar{a} \) and \( \bar{b} \).