Question

Find the angle between u=<10,6> and v=<-3,14>.

Answer 1

U
=
(
−
2
,
1
)
u
=
(
-
2
,
1
)
,
v
=
(
5
,
−
4
)
v
=
(
5
,
-
4
)
The equation for finding the angle between two vectors
θ
θ
states that the dot product of the two vectors equals the product of the magnitudes of the vectors and the cosine of the angle between them.
u
⋅
v
=
|
u
|
|
v
|
c
o
s
(
θ
)
u
⋅
v
=
|
u
|
|
v
|
c
o
s
(
θ
)
Solve the equation for
θ
θ
.
θ
=
a
r
c
⋅
c
o
s
(
u
⋅
v
|
u
|
|
v
|
)
θ
=
a
r
c
⋅
c
o
s
(
u
⋅
v
|
u
|
|
v
|
)
Find the dot product of the vectors.
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−
14
-
14
Find the magnitude of
u
u
.
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√
5
5
Find the magnitude of
v
v
.
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√
41
41
Substitute the values into the equation for the angle between the vectors.
θ
=
arccos
⎛
⎜
⎜
⎝
−
14
(
√
5
)
⋅
(
√
41
)
⎞
⎟
⎟
⎠
θ
=
arccos
(
-
14
(
5
)
⋅
(
41
)
)
Simplify.
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2.93049932
2.93049932
u
=
(
−
2
,
1
)
,
v
=
(
5
,
−
4
)
u
=
(
-
2
,
1
)
,
v
=
(
5
,
-
4
)