u
=
⟨
−
1
,
2
,
4
⟩
v
=
⟨
2
,
3
,
2
⟩
u
⋅
v
=
u
1
v
1
+
u
2
v
2
+
u
3
v
3
=
(
−
1
)
(
2
)
+
(
2
)
(
3
)
+
(
4
)
(
2
)
=
12
|
u
|
=
√
21
≈
4.583
|
v
|
=
√
17
≈
4.123
u
⋅
v
=
|
u
|
|
v
|
cos
θ
≈
(
4.583
)
(
4.123
)
(
0.688
)
≈
11.999
u
=
⟨
,
,
⟩
v
=
⟨
,
,
⟩