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Edexcel GCSE Mathematics
4. Geometry and Measures
4.3 Vectors
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Cards (61)
What is a vector in mathematics?
A quantity with magnitude and direction
What does the
x
x
x
component of a vector represent?
Movement in the horizontal direction
Vectors are equal if their
components
are equal
True
How do you add two vectors \vec{a} = \begin{pmatrix} x_1 \\ y_1 \end{pmatrix}</latex> and
b
⃗
=
\vec{b} =
b
=
(
x
2
y
2
)
\begin{pmatrix} x_{2} \\ y_{2} \end{pmatrix}
(
x
2
y
2
)
?
Add their corresponding components
What is the result of adding
a
⃗
=
\vec{a} =
a
=
(
3
4
)
\begin{pmatrix} 3 \\ 4 \end{pmatrix}
(
3
4
)
and
b
⃗
=
\vec{b} =
b
=
(
1
−
2
)
\begin{pmatrix} 1 \\ - 2 \end{pmatrix}
(
1
−
2
)
?
(
4
2
)
\begin{pmatrix} 4 \\ 2 \end{pmatrix}
(
4
2
)
What is the general form of a vector
v
⃗
\vec{v}
v
as a column matrix?
v
⃗
=
\vec{v} =
v
=
(
x
y
)
\begin{pmatrix} x \\ y \end{pmatrix}
(
x
y
)
Match the vector operation with its general formula:
Addition ↔️
a
⃗
+
\vec{a} +
a
+
b
⃗
=
\vec{b} =
b
=
\begin{pmatrix} x_{1} +
x
2
y
1
+
x_{2} \\ y_{1} +
x
2
y
1
+
y_{2} \end{pmatrix}
Subtraction ↔️
a
⃗
−
b
⃗
=
\vec{a} - \vec{b} =
a
−
b
=
(
x
1
−
x
2
y
1
−
y
2
)
\begin{pmatrix} x_{1} - x_{2} \\ y_{1} - y_{2} \end{pmatrix}
(
x
1
−
x
2
y
1
−
y
2
)
What is the result of multiplying \vec{a} = \begin{pmatrix} 3 \\ 2 \end{pmatrix}</latex> by the scalar
k
=
k =
k
=
4
4
4
?
(
12
8
)
\begin{pmatrix} 12 \\ 8 \end{pmatrix}
(
12
8
)
A vector is a quantity that has both magnitude and
direction
Vectors are often represented as column
matrices
A vector \( \vec{v} \) can be expressed as
\begin{pmatrix} x \\ y \end{pmatrix}
Match the vector component with its description:
x
x
x
↔️ Horizontal movement
y
y
y
↔️ Vertical movement
A vector has both magnitude and
direction
What does the
y
y
y
component of a vector represent?
Movement in the vertical direction
When adding vectors,
a
⃗
+
\vec{a} +
a
+
b
⃗
=
\vec{b} =
b
=
\begin{pmatrix} x_{1} +
x
2
y
1
+
x_{2} \\ y_{1} +
x
2
y
1
+
y_{2} \end{pmatrix}
, which adds the corresponding
Vectors are equal if and only if their corresponding
components
are equal.
True
What does scalar multiplication do to a vector's magnitude if the scalar is positive?
Scales the magnitude
The magnitude of a
vector
represents its length.
True
What does the vector
(
3
4
)
\begin{pmatrix} 3 \\ 4 \end{pmatrix}
(
3
4
)
represent in terms of movement?
3 units horizontally, 4 units vertically
Vectors are represented using components for horizontal and vertical movement.
True
What movement does the vector
(
3
4
)
\begin{pmatrix} 3 \\ 4 \end{pmatrix}
(
3
4
)
represent?
3 horizontal, 4 vertical
A vector \( \vec{v} \) is generally written as
\begin{pmatrix} x \\ y \end{pmatrix}
What is the general formula for adding two vectors?
a
⃗
+
\vec{a} +
a
+
b
⃗
=
\vec{b} =
b
=
\begin{pmatrix} x_{1} +
x
2
y
1
+
x_{2} \\ y_{1} +
x
2
y
1
+
y_{2} \end{pmatrix}
What is the formula for scalar multiplication of a vector?
k\vec{v} = \begin{pmatrix} kx \\ ky \end{pmatrix}</latex>
Steps to add or subtract vectors
1️⃣ Add or subtract corresponding components
2️⃣ Combine the results into a new vector
To multiply a vector
v
⃗
=
\vec{v} =
v
=
(
x
y
)
\begin{pmatrix} x \\ y \end{pmatrix}
(
x
y
)
by a scalar \(k\), multiply each component
Two vectors are parallel if they have the same magnitude.
False
What is the mathematical condition for two vectors \( \vec{a} \) and \( \vec{b} \) to be parallel?
\( \vec{a} = k\vec{b} \)
What is the additional condition for two vectors to be collinear besides being parallel?
Share a common starting point
Collinear
vectors
must have the same starting point.
True
To multiply a vector by a scalar, you only multiply one component of the vector.
False
Scalar multiplication changes the direction of a vector if the scalar is positive.
False
The
magnitude
of a vector is always a positive number.
True
Vectors are collinear if they lie on the same
line
Two vectors are parallel if they have the same magnitude.
False
Match the vector property with its description:
Direction of parallel vectors ↔️ Same or opposite
Position of collinear vectors ↔️ Must lie on the same line
The vectors \( \begin{pmatrix} 2 \\ 3 \end{pmatrix} \) and \( \begin{pmatrix} 4 \\ 6 \end{pmatrix} \) are parallel because \( \begin{pmatrix} 4 \\ 6 \end{pmatrix} = 2 \times \begin{pmatrix} 2 \\ 3 \end{pmatrix} \). The scalar \( k \) is
2
When multiplying a vector by a scalar \( k \), each component of the vector is multiplied by
k
What is the relationship between parallel and collinear vectors in terms of their direction?
Same or opposite
Match the vector property with its characteristic:
Direction of parallel vectors ↔️ Same or opposite
Position of collinear vectors ↔️ Must lie on the same line
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