A LevelMathsEdexcelMechanicsFlashcardsQuantities & Units in MechanicsWorking with Vectors

Working with Vectors (Edexcel A Level Maths: Mechanics): Flashcards

Exam code: 9MA0

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FrontWorking with Vectors
A vector describes 3 units to the right and 2 units down. Fill in the blanks:
As a column vector it is $______$
In $i$ , $j$ notation it is $______$

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Cards in this collection (7)

A vector describes 3 units to the right and 2 units down. Fill in the blanks:
As a column vector it is $______$
In $i$ , $j$ notation it is $______$
The completed forms are:
As a column vector it is $(\begin{matrix} 3 \\ - 2 \end{matrix})$
In $i$ , $j$ notation it is $3 i - 2 j$
Both describe the same vector. The top number of the column vector is the horizontal component and matches the $i$ term, and the bottom number is the vertical component and matches the $j$ term. Down is the negative vertical direction, which is why the second component is negative.
In $i$ , $j$ notation, what are $i$ and $j$ ?
$i$ and $j$ are unit vectors, which means each has a magnitude of 1.
$i$ points in the positive horizontal direction and $j$ in the positive vertical direction.
So $5 i$ means 5 units to the right, and $- 4 i$ means 4 units to the left.
Define the modulus of a vector.
The modulus of a vector is its magnitude: its size, with no direction attached.
It is written with vertical bars, so the modulus of $a$ is written $|a|$ .
A modulus is a length, so it is never negative, whatever the signs of the components it was calculated from.
A question asks for the direction of a resultant force as a bearing. What is a bearing measured from, and in which direction is it measured?
A bearing is measured from north, turning clockwise, and is written with three figures.
That is a different convention from an angle measured anticlockwise from the positive horizontal, so the two give different numbers for the same vector and you must check which the question wants.
A vector pointing due west has a bearing of $270 \circ$ , but its direction measured anticlockwise from the positive horizontal is $180 \circ$ .
In a bearings question the unit vectors stand for compass directions. Fill in the blanks:
$______$ represents north
$______$ represents east
The completed statements are:
$j$ represents north
$i$ represents east
So a particle moving due north has a velocity of the form $k j$ with $k > 0$ , and a particle moving due west has a velocity of the form $- k i$ .
Particle $A$ is due south of particle $B$ . What form does the displacement vector from $B$ to $A$ take?
The displacement from $B$ to $A$ has the form $- k j$ , where $k > 0$ .
South is the negative $j$ direction, since $j$ represents north.
There is no east-west component at all, so the $i$ component is zero, which is what "due south" adds to "south of".
True or False?
If a particle's position vector has equal $i$ and $j$ components, the particle is north-east of the origin.
False.
It is north-east of the origin only when both components are positive, such as $4 i + 4 j$ .
Equal negative components, such as $- 4 i - 4 j$ , put the particle south-west of the origin instead, and components that are both zero put it at the origin itself.
What equal components really tell you is that the particle lies on a line at $45 °$ to both axes.

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