A vector is a type of number with both size and direction . For example, a vector could represent "4 units to the right".

What is the difference between a vector and a scalar ?

A vector has a direction , whereas a scalar is just a number with no direction .

What is meant by the modulus (magnitude) of a vector?

The modulus (magnitude) of a vector is its length .

True or False? If two vectors are parallel , then they are scalar multiples .

True. If two vectors are parallel , then they are scalar multiples .

IGCSEMaths A: HigherEdexcelFlashcards

Vectors (Edexcel IGCSE Maths A)

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FrontIntroduction to Vectors
What is a vector?

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What is a vector?
A vector is a type of number with both size and direction.
For example, a vector could represent "4 units to the right".
What is the difference between a vector and a scalar?
A vector has a direction, whereas a scalar is just a number with no direction.
True or False?
$\vec{A B}$ represents the vector from $A$ to $B$ .
True.
$\vec{A B}$ represents the vector from $A$ to $B$ .
True or False?
The vector $(\begin{matrix} 2 \\ 3 \end{matrix})$ must be drawn starting at $(0, 0)$ and ending at the point $(2, 3)$ .
False.
The vector $(\begin{matrix} 2 \\ 3 \end{matrix})$ does not need to be drawn starting at $(0, 0)$ and ending at the point $(2, 3)$ .
The vector can start at any point, as long as it goes 2 to the right and 3 up.
How do you write "3 to the left and 2 up" as a column vector?
"3 to the left and 2 up" can be written as the column vector $(\begin{matrix} - 3 \\ 2 \end{matrix})$ .
How do you add two column vectors?
To add two column vectors, add together the numbers in the corresponding parts of the vector.
For example, $(\begin{matrix} 1 \\ 2 \end{matrix}) + (\begin{matrix} 3 \\ - 5 \end{matrix}) = (\begin{matrix} 1 + 3 \\ 2 + (- 5) \end{matrix}) = (\begin{matrix} 4 \\ - 3 \end{matrix})$ .
True or False?
$5 \times (\begin{matrix} 3 \\ 4 \end{matrix}) = (\begin{matrix} 15 \\ 4 \end{matrix})$
False.
$5 \times (\begin{matrix} 3 \\ 4 \end{matrix}) \neq (\begin{matrix} 15 \\ 4 \end{matrix})$ .
To multiply a vector by a scale, you need to multiply all parts of the vector by the scalar.
$5 \times (\begin{matrix} 3 \\ 4 \end{matrix}) = (\begin{matrix} 15 \\ 20 \end{matrix})$ .
If you know what the vectors $a$ and $b$ look like, how could you draw the vector $a + b$ ?
If you know what the vectors $a$ and $b$ look like, to draw the vector $a + b$ :
- Draw the vector $a$
- Draw the vector $b$ starting at the end of $a$
- Draw a vector from the start of $a$ to the end of $b$
True or False?
The vector $2 a$ is in the same direction as $a$ but it is double the length.
True.
The vector $2 a$ is in the same direction as $a$ but it is double the length.
Scalar multiples of a vector change the length of the vector.
What is the geometrical relationship between the vectors $a$ and $- a$ ?
The vectors $a$ and $- a$ have the same length but they are in opposite directions.
What is meant by the modulus (magnitude) of a vector?
The modulus (magnitude) of a vector is its length.
True or False?
The modulus of the vector $(\begin{matrix} 2 \\ 3 \end{matrix})$ is $2^{2} + 3^{2}$ .
False.
The modulus of the vector $(\begin{matrix} 2 \\ 3 \end{matrix})$ is not $2^{2} + 3^{2}$ .
To find the modulus of a vector, you square the numbers, add them together and them take the positive square root.
The modulus of the vector $(\begin{matrix} 2 \\ 3 \end{matrix})$ is $\sqrt{2^{2} + 3^{2}}$ .
True or False?
The modulus of the vector $(\begin{matrix} 2 \\ - 3 \end{matrix})$ is $\sqrt{2^{2} - 3^{2}}$ .
False.
The modulus of the vector $(\begin{matrix} 2 \\ - 3 \end{matrix})$ is not $\sqrt{2^{2} - 3^{2}}$ .
You need to square the negative in front of the 3.
The modulus of the vector $(\begin{matrix} 2 \\ - 3 \end{matrix})$ is $\sqrt{2^{2} + {(- 3)}^{2}}$ .
True or False?
If two vectors are parallel, then they are scalar multiples.
True.
If two vectors are parallel, then they are scalar multiples.
True or False?
$\vec{A B} + \vec{B C} = \vec{A C}$
True.
$\vec{A B} + \vec{B C} = \vec{A C}$
This means if you start at A then go to B and then go to C, this is the same vector as starting at A and going to C.
How else could you write the vector $- \vec{A B}$ ?
The vector $- \vec{A B}$ can also be written as $\vec{B A}$ .
True or False?
$\vec{A B} = \vec{O A} - \vec{O B}$
False.
$\vec{A B} \neq \vec{O A} - \vec{O B}$
The correct equation is $\vec{A B} = \vec{O B} - \vec{O A}$ .
A and B have position vectors, $a$ and $b$ .
Write a formula for the position vector of the midpoint of A and B in terms of $a$ and $b$ .
A and B have position vectors, $a$ and $b$ .
A formula for the position vector of the midpoint of A and B is $\frac{1}{2} (a + b)$ .
True or False?
If the point P divides the line AB in the ratio 1 : 3, then $\vec{A P} = \frac{1}{3} \vec{A B}$ .
False.
If the point P divides the line AB in the ratio 1 : 3, then $\vec{A P} \neq \frac{1}{3} \vec{A B}$ .
P divides the line into 4 equal parts, two points on one side, and 3 parts on the other side.
The correct equation is $\vec{A P} = \frac{1}{4} \vec{A B}$ .
If the vectors $\vec{A B}$ and $\vec{A C}$ are parallel, what does this tell you at the three points, $A$ , $B$ and $C$ ?
If the vectors $\vec{A B}$ and $\vec{A C}$ are parallel, then the three points, $A$ , $B$ and $C$ all lie on the same straight line.

1. Numbers & the Number System

2. Equations, Formulae & Identities

3. Sequences, Functions & Graphs

4. Geometry & Trigonometry

5. Vectors & Transformation Geometry

6. Statistics & Probability