Determine whether the statement is true or false. Show proof.
A)For any vectors u and v in V3, |u + v| = |u| + |v|.
B)For any vectors u and v in V3, |u · v| = |u||v|.
C)For any vectors u and
Determine whether the statement is true or false.
Show proof.
A)For any vectors u and v in V₃, |u + v| = |u| + |v|.
B)For any vectors u and v in V₃, |u · v| = |u||v|.
C)For any vectors u and v in V₃, u × v = v × u.
D)For any vectors u, v, and w in V₃, u × (v × w) = (u × v) × w.
E)If u · v = 0, then u = 0 or v = 0.
F)If u × v = 0, then u = 0 or v = 0.
G)If |r(t)| = 1 for all t, then |r'(t)| is a constant.
H)If u(t) and v(t) are differentiable vector functions, then
d
dt
[u(t) × v(t)] = u'(t) × v'(t).