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Unit Vectors
Related Topics
Wize University Linear Algebra Textbook > Vectors
Unit Vectors
3 Activities
Practice: Unit Vectors
Find the value of
k
k
k
such that
u
⃗
=
⟨
k
,
1
2
,
−
k
⟩
\vec u = \left\lang k, \dfrac{1}{\sqrt2}, -k \right\rang
u
=
⟨
k
,
2
1
,
−
k
⟩
is a unit vector.
A)
1
2
\dfrac{1}{2}
2
1
B)
±
1
2
\pm\dfrac{1}{2}
±
2
1
C)
1
2
\dfrac{1}{\sqrt{2}}
2
1
D)
±
1
2
\pm\dfrac{1}{\sqrt{2}}
±
2
1
E) None of the above
I don't know
Check Submission
More Unit Vectors Questions:
Find the unit vector in the opposite direction as
𝑣
⃗
=
(
1
,
−
1
,
0
,
−
1
,
0
)
𝑣⃗\ =(1,−1,0,−1,0)
v
⃗
=
(
1
,
−
1
,
0
,
−
1
,
0
)
Find the unit vector in the same direction as
v
⃗
=
(
1
,
0
,
−
3
,
4
,
−
2
)
\vec{v}=\left(1,\ 0,\ -3,\ 4,\ -2\right)
v
=
(
1
,
0
,
−
3
,
4
,
−
2
)
.
Vectors in 2D and 3D Systems (2)
Practice
Find the unit vector that points in the same direction as
a
⃗
=
<
−
10
,
4
,
−
3
>
\vec{a}~=<-10,~4,~-3>
a
=<
−
10
,
4
,
−
3
>
.
133 - FML 3 - 18.1W e.g. 26
Find on expression for a vector of unit length in the direction of
v
⃗
=
<
v
1
,
v
2
,
v
3
>
\bcb{\vec{v} = \left< v_1, v_2, v_3 \right>}
v
=
⟨
v
1
,
v
2
,
v
3
⟩
.
Practice: Unit Vector
Practice: Unit Vectors
Find the unit vector in the same direction as
v
⃗
=
(
1
,
−
2
,
−
1
)
\vec v = (1,-2,-1)
v
=
(
1
,
−
2
,
−
1
)
.
Practice: Unit Vector
Practice: Unit Vector
Find the unit vector in the same direction as
i
⃗
−
5
k
⃗
\vec i-5\vec k
i
−
5
k
.
Practice: Unit Vector
Practice: Unit Vector
Find the unit vector in the same direction as
i
^
−
5
k
^
\hat{i}-5\hat{k}
i
^
−
5
k
^
.
Concept Clarifier
Find the unit vector in the direction of
v
⃗
=
(
3
,
4
,
5
)
\vec{v}=(3,4,5)
v
=
(
3
,
4
,
5
)
Practice: Cross Product
Practice: Cross Product
Consider
u
⃗
=
[
−
2
,
3
,
−
1
]
\vec{u}=\left[-2,\ 3,\ -1\right]
u
=
[
−
2
,
3
,
−
1
]
and
v
⃗
=
[
1
,
0
,
−
1
]
\vec{v}=\left[1,\ 0,\ -1\right]
v
=
[
1
,
0
,
−
1
]
.
133 - FML 3 - 18.1W e.g. 24
If a vector
v
⃗
\bcb{\vec{v}}
v
has length
L
\bcb{\mathcal{L}}
L
, give an expression for a unit vector in the same direction as
v
⃗
\bcb{\vec{v}}
v
.
133 - FML 3 - 18.1W e.g. 26
Find an expression for a vector of unit length in the direction of
v
⃗
=
<
v
1
,
v
2
,
v
3
>
\bcb{\vec{v} = \left< v_1, v_2, v_3 \right>}
v
=
⟨
v
1
,
v
2
,
v
3
⟩
.
133 - FML 3 - 18.1W e.g. 48
Find a unit vector in the direction of the projection of
u
⃗
=
<
102
,
112
,
−
56
>
\bcb{\vec{u} = \left< 102, 112, -56 \right>}
u
=
⟨
102
,
112
,
−
56
⟩
onto
v
⃗
=
<
0
,
3
,
4
>
\bcb{\vec{v} = \left< 0, 3, 4 \right>}
v
=
⟨
0
,
3
,
4
⟩
.
133 - FML 3 - 18.1W e.g. 24
If a vector
v
⃗
\bcb{\vec{v}}
v
has length
L
\bcb{\mathcal{L}}
L
, give an expression for a unit vector in the same direction as
v
⃗
\bcb{\vec{v}}
v
.
$\tkct{cut from 19.4F}$ Mid $\tkco{ S}$ | 133 - FML 3 - 18.1W e.g. 48
Find a unit vector in the direction of the projection of
u
⃗
=
<
102
,
112
,
−
56
>
\bcb{\vec{u} = \left< 102, 112, -56 \right>}
u
=
⟨
102
,
112
,
−
56
⟩
onto
v
⃗
=
<
0
,
3
,
4
>
\bcb{\vec{v} = \left< 0, 3, 4 \right>}
v
=
⟨
0
,
3
,
4
⟩
.
Concept Clarifier
Find the unit vector in the direction of
v
⃗
=
(
3
,
4
,
5
)
\vec{v}=(3,4,5)
v
=
(
3
,
4
,
5
)
Unit Vector Practice Question
Find the unit vector in the same direction as
v
⃗
=
(
3
,
4
,
5
)
\vec{v}=(3,4,5)
v
=
(
3
,
4
,
5
)
Practice Question: Unit Vector
Practice Question: Unit Vector
Find the unit vector in the same direction as 𝑣 = (1, −2, −1).
Practice Question: Unit Vector
Practice Question: Unit Vector
Find the unit vector in the same direction as 𝑣 = (1, −2, −1).
Practice Question: Unit Vector
Practice Question: Unit Vector
Which one of the following is not a unit vector?
Practice Question: Unit Vector
Practice Question: Unit Vector
Find the unit vector in the opposite direction as
𝑣
⃗
=
(
1
,
−
1
,
0
,
−
1
,
0
)
𝑣⃗\ =(1,−1,0,−1,0)
v
⃗
=
(
1
,
−
1
,
0
,
−
1
,
0
)
.
Practice: Unit Vector
Practice: Unit Vector
Find the unit vector in the same direction as 𝑣 = (1, −2, −1).
Practice: Unit Vector
Practice: Unit Vector
Find the unit vector in the same direction as
i
⃗
−
5
k
⃗
\vec i-5\vec k
i
−
5
k
.
$\tkcth{Moved }\bcth{\to} \key{ Mid} \tkco{ S } \tkcth{ch 3 quiz ✓}$ |
A unit vector parallel to the vector
v
⃗
=
<
4
,
−
3
>
\vv = \rowvec{4}{-3}
v
=
⟨
4
,
−
3
⟩
is:
$\tkcth{Moved }\bcth{\to} \key{ Mid} \tkco{ S } \tkcth{ch 3 quiz ✓}$ |
A unit vector perpendicular to the vector
w
⃗
=
<
2
,
5
>
\vw = \rowvec{2}{5}
w
=
⟨
2
,
5
⟩
is:
$\tkcth{Moved }\bcth{\to} \key{ Mid} \tkco{ S } \tkcth{ch 3 quiz ✓}$ |
Find a vector parallel to the vector
u
⃗
=
<
1
,
4
,
8
>
\vu = \rowvecth{1}{4}{8}
u
=
⟨
1
,
4
,
8
⟩
whose magnitude is 1.
DIY Unit Vector
Find a vector whose length is one, that points in the same direction as the vector
u
⃗
=
<
2
,
1
,
−
2
>
\vu = \rowvecth{2}{1}{-2}
u
=
⟨
2
,
1
,
−
2
⟩
Unit Vectors: Dot Product
Consider the vectors
u
=
i
−
4
k
\bm{u}=\bm{i}-4\bm{k}
u
=
i
−
4
k
and
v
=
3
i
−
2
j
+
k
\bm{v}=3\bm{i}-2\bm{j}+\bm{k}
v
=
3
i
−
2
j
+
k
in
R
3
\reals^3
R
3
. Find (if possible)
3
v
⋅
(
k
−
2
u
)
3\bm{v}\cdot(\bm{k}-2\bm{u})
3
v
⋅
(
k
−
2
u
)
.