igureMaths
Log in
Start free
←
Vectors
Get dealt questions instead
→
Browse Vectors
39 questions at your level
Difficulty
All
Level 1
Level 2
Level 3
Level 4
Level 5
Column vectors
16 questions
Lesson
Not started
Mark as done
a
=
(
5
−
2
)
\mathbf{a} = \binom{5}{-2}
a
=
(
−
2
5
)
and
b
=
(
−
3
4
)
\mathbf{b} = \binom{-3}{4}
b
=
(
4
−
3
)
.
(a)
Work out
a
+
b
\mathbf{a} + \mathbf{b}
a
+
b
as a column vector.
(b)
Work out
a
−
b
\mathbf{a} - \mathbf{b}
a
−
b
as a column vector.
(c)
Work out
3
b
3\mathbf{b}
3
b
as a column vector.
●●
●●●
Level 2
3 marks
Start
→
Mark as done
a
=
(
2
3
)
\mathbf{a} = \begin{pmatrix} 2 \\ 3 \end{pmatrix}
a
=
(
2
3
)
and
b
=
(
−
1
4
)
\mathbf{b} = \begin{pmatrix} -1 \\ 4 \end{pmatrix}
b
=
(
−
1
4
)
(a)
Work out
a
−
b
\mathbf{a} - \mathbf{b}
a
−
b
(1 mark)
(b)
Work out
3
a
+
2
b
3\mathbf{a} + 2\mathbf{b}
3
a
+
2
b
(1 mark)
(c)
P
P
P
is the point
(
1
,
2
)
(1, 2)
(
1
,
2
)
and
Q
Q
Q
is the point
(
4
,
8
)
(4, 8)
(
4
,
8
)
. Write
P
Q
→
\overrightarrow{PQ}
P
Q
as a column vector. (1 mark)
●●
●●●
Level 2
3 marks
Start
→
Mark as done
a
=
(
3
−
2
)
\mathbf{a} = \begin{pmatrix} 3 \\ -2 \end{pmatrix}
a
=
(
3
−
2
)
and
b
=
(
−
1
4
)
\mathbf{b} = \begin{pmatrix} -1 \\ 4 \end{pmatrix}
b
=
(
−
1
4
)
(a)
Work out
2
a
+
b
2\mathbf{a} + \mathbf{b}
2
a
+
b
as a column vector. (1 mark)
(b)
Work out the magnitude of
a
\mathbf{a}
a
. Give your answer correct to 3 significant figures. (2 marks)
●●
●●●
Level 2
3 marks
Start
→
Mark as done
a
=
(
3
1
)
\mathbf{a} = \begin{pmatrix} 3 \\ 1 \end{pmatrix}
a
=
(
3
1
)
and
b
=
(
−
2
4
)
\mathbf{b} = \begin{pmatrix} -2 \\ 4 \end{pmatrix}
b
=
(
−
2
4
)
(a)
Work out
2
a
−
b
2\mathbf{a} - \mathbf{b}
2
a
−
b
[1]
(b)
Write down the exact magnitude of
a
\mathbf{a}
a
. [1]
(c)
P
P
P
is
(
−
1
,
2
)
(-1, 2)
(
−
1
,
2
)
and
Q
Q
Q
is
(
3
,
−
4
)
(3, -4)
(
3
,
−
4
)
. Write
P
Q
→
\overrightarrow{PQ}
P
Q
as a column vector. [1]
(d)
Show that
(
6
2
)
\begin{pmatrix} 6 \\ 2 \end{pmatrix}
(
6
2
)
is parallel to
a
\mathbf{a}
a
. [1]
●●
●●●
Level 2
4 marks
Start
→
Vectors on a shape
13 questions
Lesson
Not started
Mark as done
P
Q
R
S
PQRS
P
QR
S
is a parallelogram.
P
Q
→
=
a
\overrightarrow{PQ} = \mathbf{a}
P
Q
=
a
and
P
S
→
=
b
\overrightarrow{PS} = \mathbf{b}
P
S
=
b
.
a
b
P
Q
R
S
The diagram is a sketch and is not accurately drawn.
(a)
Write down, in terms of
a
\mathbf{a}
a
and/or
b
\mathbf{b}
b
, the vector
S
R
→
\overrightarrow{SR}
S
R
.
(b)
Give a reason for your answer to part (a).
(c)
Find
Q
S
→
\overrightarrow{QS}
QS
in terms of
a
\mathbf{a}
a
and
b
\mathbf{b}
b
.
●●
●●●
Level 2
4 marks
Start
→