How do you add vectors in component form?

Add the \mathbf{i} components and add the \mathbf{j} components.

What is the resultant of a set of forces?

The single force with the same effect as all of them acting together.

What is true of the resultant when a particle is in equilibrium?

It is zero: \mathbf{R}=\mathbf{0}.

How do you write a vector of magnitude M in the direction of x\mathbf{i}+y\mathbf{j}?

M\dfrac{x\mathbf{i}+y\mathbf{j}}{\sqrt{x^2+y^2}}

What does the triangle law say?

Place vectors nose to tail; the resultant joins the start to the end.

Vectors and resultantsEdexcel International A Level Maths: Flashcards

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What is a vector?

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What is a vector?: A quantity with both magnitude and direction.
What is a scalar?: A quantity with magnitude only.
Magnitude of $x\mathbf{i}+y\mathbf{j}$ ?: $\sqrt{x^2+y^2}$
Angle of $x\mathbf{i}+y\mathbf{j}$ with $\mathbf{i}$ ?: $\tan\theta=\dfrac{y}{x}$
How do you add vectors in component form?: Add the $\mathbf{i}$ components and add the $\mathbf{j}$ components.
What is the resultant of a set of forces?: The single force with the same effect as all of them acting together.
What is true of the resultant when a particle is in equilibrium?: It is zero: $\mathbf{R}=\mathbf{0}$ .
Component of $F$ at $\theta$ to $\mathbf{i}$ along $\mathbf{i}$ ?: $F\cos\theta$
Component of $F$ at $\theta$ to $\mathbf{i}$ along $\mathbf{j}$ ?: $F\sin\theta$
What is $3\mathbf{i}+4\mathbf{j}$ in magnitude?: $\sqrt{9+16}=5$
How do you write a vector of magnitude $M$ in the direction of $x\mathbf{i}+y\mathbf{j}$ ?: $M\dfrac{x\mathbf{i}+y\mathbf{j}}{\sqrt{x^2+y^2}}$
What does the triangle law say?: Place vectors nose to tail; the resultant joins the start to the end.

Exam questions on Vectors and resultants

Two forces act on a particle: $\mathbf{F}_1=(7\mathbf{i}-3\mathbf{j})$ N and $\mathbf{F}_2=(-2\mathbf{i}+6\mathbf{j})$ N, where $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors in the horizontal plane, in the directions east and north.
Find the angle between the resultant force and the direction east, giving your answer in degrees to 1 decimal place.2 marks
A force $\mathbf{F}$ of magnitude 24 N acts on a particle in a direction $40^\circ$ above the direction of the unit vector $\mathbf{i}$ , where $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors in a vertical plane, horizontal and vertically upwards respectively.
A second force $\mathbf{G}=(-10\mathbf{i}-6\mathbf{j})$ N also acts on the particle. Find the magnitude of the resultant of $\mathbf{F}$ and $\mathbf{G}$ .2 marks
Three forces $\mathbf{P}=(3\mathbf{i}+5\mathbf{j})$ N, $\mathbf{Q}=(-7\mathbf{i}+2\mathbf{j})$ N and $\mathbf{R}=(p\mathbf{i}+q\mathbf{j})$ N act on a particle, where $p$ and $q$ are constants. The particle is in equilibrium.
Find the values of $p$ and $q$ .3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).