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Find the vector u which has the opposite direction as v=1-82^T but half the len…
Related Topics
Wize University Linear Algebra Textbook > Vectors
Basics of Vectors
4 Activities
Find the vector
u
⃗
\vec{u}
u
which has the opposite direction as
v
⃗
=
[
1
−
8
2
]
T
\vec{v}=\begin{bmatrix}1&-8&2\end{bmatrix}^T
v
=
[
1
−
8
2
]
T
but half the length.
u
⃗
=
[
1
/
2
4
1
]
\vec{u}=\begin{bmatrix}1/2\\4\\1\end{bmatrix}
u
=
1/2
4
1
u
⃗
=
[
−
1
4
−
1
]
\vec{u}=\begin{bmatrix}-1\\4\\-1\end{bmatrix}
u
=
−
1
4
−
1
u
⃗
=
[
−
1
/
2
4
−
1
]
\vec{u}=\begin{bmatrix}-1/2\\4\\-1\end{bmatrix}
u
=
−
1/2
4
−
1
u
⃗
=
[
1
/
2
−
4
−
1
]
\vec{u}=\begin{bmatrix}1/2\\-4\\-1\end{bmatrix}
u
=
1/2
−
4
−
1
I don't know
Check Submission
More Basics of Vectors Questions:
Basics of Vectors
Practice: Basics of Vectors
Examine the following graph.
Find the vector
u
⃗
\vec{u}
u
which has the opposite direction as
v
⃗
=
[
1
−
8
2
]
T
\vec{v}=\begin{bmatrix}1&-8&2\end{bmatrix}^T
v
=
[
1
−
8
2
]
T
but half the length.
Given the points
A
(
0
,
−
1
,
3
)
A\left(0,-1,3\right)
A
(
0
,
−
1
,
3
)
and
B
(
5
,
−
6
,
−
2
)
B\left(5,-6,-2\right)
B
(
5
,
−
6
,
−
2
)
, find
B
A
⃗
+
A
B
⃗
\vec{BA}+\vec{AB}
B
A
+
A
B
.
*Type any vector answers in the form (a, b, c)
special unit vector concept clarifier
Wize Concept Clarifier:
Express
𝑣
⃗
=
(
15
,
0
,
−
2
)
\vec{𝑣} = (15, 0, −2)
v
=
(
15
,
0
,
−
2
)
i
n terms of special unit vectors
The coordinates of four corners of a Parallelogram
A
B
C
D
ABCD
A
B
C
D
in a Clock-Wise order are
A
=
(
1
,
3
)
A=(1,3)
A
=
(
1
,
3
)
,
B
=
(
−
1
,
5
)
B=(-1,5)
B
=
(
−
1
,
5
)
,
C
C
C
and
D
=
(
4
,
7
)
D=(4,7)
D
=
(
4
,
7
)
. Find missing coordinates of
C
C
C
.
Concept Clarifier
The coordinates of four corners of a Parallelogram
A
B
C
D
ABCD
A
B
C
D
in a Clock-Wise order are
A
=
(
1
,
3
)
A=(1,3)
A
=
(
1
,
3
)
,
B
=
(
−
1
,
5
)
B=(-1,5)
B
=
(
−
1
,
5
)
,
C
C
C
and
D
=
(
4
,
7
)
D=(4,7)
D
=
(
4
,
7
)
. Find missing coordinates of
C
C
C
.
Practice: Scalar or Vector?
Each of the following is either a scalar or a vector quantity.
Select
all
of the
vector quantities
in the list.
Fill in the blanks.
A vector quantity has both a ____[A]____ and a ____[B]______ while while scalar quantities have only a _____[C]______
Practice Question: Direction Vector
Practice Question: Direction Vector
Which of the following vectors is not parallel to the line passing through the points
(
1
,
2
)
a
n
d
(
−
3
,
4
)
?
(1,2)\ and\ (−3,4)?
(
1
,
2
)
an
d
(
−
3
,
4
)?
a.)
(
5
,
−
5
2
)
\left(5,\ -\frac{5}{2}\right)
(
5
,
−
2
5
)
Practice: Vector Properties
Given the points
A
(
1
,
−
3
,
2
)
A\left(1,\ -3,2\right)
A
(
1
,
−
3
,
2
)
,
B
(
0
,
1
,
1
)
B\left(0,\ 1,\ 1\right)
B
(
0
,
1
,
1
)
,
C
(
4
,
−
15
,
5
)
C\left(4,\ -15,\ 5\right)
C
(
4
,
−
15
,
5
)
, wich of the following statements is/are true?
(Select all that apply)
Practice: Vector Operations
A parallelogram has sides
A
B
AB
A
B
,
B
C
BC
B
C
,
C
D
CD
C
D
and
D
A
DA
D
A
The following coordinates are known:
A
(
2
,
0
,
1
)
A(2,0,1)
A
(
2
,
0
,
1
)
,
C
(
6
,
0
,
0
)
C(6,0,0)
C
(
6
,
0
,
0
)
, and
M
(
3
,
1
,
0
)
M(3,1,0)
M
(
3
,
1
,
0
)
, where
M
M
M
is the midpoint between
A
A
A
and
B
B
B
Find the vector
B
D
⃗
\vec{BD}
B
D
$\tkcth{Moved }\bcth{\to} \key{ Mid} \tkco{ S } \tkcth{ch 3 quiz ✓}$ | Proofed. 19.1W
The vector going
from
the point
P
1
(
−
1
,
1
,
−
4
)
P_1(-1,1,-4)
P
1
(
−
1
,
1
,
−
4
)
to
the point
P
2
(
1
,
4
,
2
)
P_2(1,4,2)
P
2
(
1
,
4
,
2
)
is:
Practice: 2D Vectors
Practice: 2D Vectors
Given the diagram below, answer the following questions.