SUPPLEMENTARY PROBLEMS
Vectors in \( \mathbf{R}^{\boldsymbol{n}} \)
1.41. Let \( u=(1,-2,4), v=(3,5,1), w=(2,1,-3) \). Find:
(a) \( 3 u-2 v \);
(b) \( 5 u+3 v-4 w \);
(c) \( u \cdot v, u \cdot w, \quad v \cdot w \);
(d) \( \|u\|,\|v\| \)
(e) \( \cos \theta \), where \( \theta \) is the angle between \( u \) and \( v \);
(f) \( d(u, v) \)
(g) \( \operatorname{proj}(u, v) \).