5.1.2

Vectors 2

Test yourself on Vectors 2

Test your knowledge with free interactive questions on Seneca — used by over 10 million students.

Scalars and Straight Lines

A scalar is any number such as 10, π, -4, 1⁄2, 4.52, √6.

Scalars and vectors

Scalars and vectors

  • When a vector is multiplied by a scalar its direction does not change but its size does.
  • A negative scalar switches the direction of the vector.
  • To multiply a column vector by a scalar multiply both top and bottom numbers by the scalar.
Straight lines

Straight lines

  • To show 3 points A, B and C lie in a straight line show that AB is a scalar multiple of BC.
Ratios and lengths

Ratios and lengths

  • If given side lengths in ratios you can translate this to vector form.
    • If AB : BC = 2 : 3 and A, B, C are in a straight line then 2 AB = 3 BC.

Magnitude of Vectors

Vectors have a magnitude (size) and direction. The magnitude of a vector can be calculated from the column vector.

Calculating the magnitude

Calculating the magnitude

  • You can use Pythagoras' theorem to calculate the magnitude of a vector (xy\large{x}\atop{y}).
  • The magnitude of a vector (xy)({\large{x}\atop{y}}) is x2+y2\sqrt{x^2+y^2}.
Vector notation

Vector notation

  • You will need to be careful when writing vectors in your exam.
  • Vectors will be printed on the exam as AB⃗\vec{AB} or a.
  • The magnitude of a vector will be shown using modulus signs.
    • I.e. magnitude of AB⃗\vec{AB} = |AB⃗\vec{AB}|
    • I.e. magnitude of a = |a|
Using vector notation

Using vector notation

  • In your exam, you will need to show the examiner that you know the difference between the vector a and the letter a.
  • There are two ways to do this:
    • Using an arrow above the vector, e.g. AB⃗\vec{AB}
    • Underlining the letter, e.g. a‾\underline{a}

Proof by Vector Method

Vectors can be used to prove geometric properties of shapes.

Example

Example

  • By method of vectors, prove that STU is a straight line.
Draw the diagram

Draw the diagram

  • Remember to label each points carefully.
Work out the vectors

Work out the vectors

  • Work out the vectors for the points connecting the path from S to T to U, in terms of the vectors p and q.
Compare

Compare

  • Compare the vector ST with the vector TU.
  • If STU is a straight line, then ST and TU will be multiples of one another with T as a common point.
Jump to other topics
1

Numbers

1.1

Integers

1.1.1Integers1.1.2Ordering Numbers1.1.3The Four Rules of Operations1.1.4Hierarchy of Operations1.1.5Definitions & Terms1.1.6HCF & LCM1.1.7Standard Form1.1.8Standard Form 21.1.9Prime Numbers1.1.10End of Topic Test - Standard Form
1.2

Fractions

1.2.1Fractions1.2.2Using Fractions1.2.3Conversion1.2.4Reciprocals
1.3

Decimals

1.3.1Decimals1.3.2Decimals 21.3.3Exam-Style Questions - Recurring Decimals1.3.4Comparing & Converting Decimals1.3.5End of Topic Test - Fractions & Decimals
1.4

Powers & Roots

1.4.1Square Numbers1.4.2Index Notation1.4.3Exam-Style Questions - Index Notation1.4.4Advanced Indices1.4.5Surds1.4.6End of Topic Test - Powers & Roots
1.5

Set Language & Notation

1.5.1Sets
1.6

Percentages

1.6.1Percentages1.6.2Percentage Change1.6.3Percentages in Finance1.6.4Compound Interest
1.7

Ratio & Proportion

1.7.1Manipulating Ratios1.7.2Proportion
1.8

Degree of Accuracy

1.8.1Rounding & Significant Figures1.8.2Estimation1.8.3Upper & Lower Bounds1.8.4Limits of Accuracy1.8.5Limits of Accuracy 21.8.6End of Topic Test - Rounding & Estimation
2

Equations, Formulae & Identities

2.1

Algebraic Manipulation

2.1.1Algebra Basics2.1.2Power Rules & Collecting Terms2.1.3Expanding Brackets2.1.4Expanding Brackets 22.1.5Factorising Quadratics2.1.6Algebraic Fractions2.1.7Proofs2.1.8End of Topic Test - Algebra & Proofs2.1.9Exam-Style Questions - Algebraic Proof
2.2

Expressions & Formulae

2.2.1Rearranging Formulae2.2.2Simple Formulae2.2.3End of Topic Test - Algebra Manipulation & Formula
2.3

Linear Equations

2.3.1Solving Linear Equations2.3.2Simultaneous Linear Equations
2.4

Quadratic Equations

2.4.1Solving Quadratics2.4.2Solving Quadratics 22.4.3End of Topic Test - Solving Equations2.4.4Simulateous Quadratic Equations2.4.5Exam-Style Questions - Simultaneous Equations2.4.6Graphs of Simultaneous Equations2.4.7End of Topic Test - Simultaneous Equations
2.5

Proportion

2.5.1Graphs & Proportion
2.6

Inequalities

2.6.1Solving Inequalities2.6.2Graphs of Inequalities2.6.3Exam-Style Questions - Inequalities2.6.4End of Topic Test - Inequalities
3

Sequences, Functions & Graphs

3.1

Sequences

3.1.1Sequence Rules3.1.2Finding Terms3.1.3Exam-Style Questions - Sequences3.1.4End of Topic Test - Sequences
3.2

Functions

3.2.1Functions3.2.2Composite & Inverse3.2.3End of Topic Test - Functions
3.3

Graphs

3.3.1Plotting Graphs3.3.2Straight Line Graphs3.3.3Properties of Graphs3.3.4Quadratic Graphs3.3.5Practical Graphs3.3.6Graphs of Polynomials3.3.7End of Topic Test Graphs
3.4

Common Graphs

3.4.1Graphs of Common Functions3.4.2Transformations of Graphs3.4.3End of Topic Test - Transformations and Graph
3.5

Calculus

3.5.1Derivatives of Functions3.5.2Maxima & Minima
4

Geometry

4.1

Angles, Lines & Triangles

4.1.1Angles & Lines4.1.2Angle Rules4.1.3Angles in Triangles4.1.4Exam-Style Questions - Angles
4.2

Polygons

4.2.1Polygons4.2.2Quadrilaterals4.2.3Congruence4.2.4Scale Factor4.2.5Exam-Style Questions - Enlargements4.2.6End of Topic Test - Geometry
4.3

Symmetry

4.3.1Symmetry4.3.2Exam-Style Questions - Reflection
4.4

Measures

4.4.1Measurements4.4.2Time4.4.3Bearings4.4.4Speed
4.5

Circle Properties

4.5.1Properties of a Circle4.5.2Circle Theorems4.5.3Circle Theorems 24.5.4Circle Theorems 34.5.5Exam-Style Questions - Circle Theorems
4.6

Trigonometry & Pythagoras’ theorem

4.6.1Pythagoras' Theorem4.6.2Trigonometry4.6.3Sine & Cosine for Obtuse Angles4.6.4Triangle Formulae4.6.5Exam-Style Questions - Trigonometry & Area
4.7

Mensuration of 2D Shapes

4.7.1Standard Units4.7.2Perimeter of 2D Shapes4.7.3Area of 2D Shapes4.7.4Area & Circumference of Circle4.7.5End of Topic Test - Trigonometry & Shapes
4.8

3D Shapes & Volume

4.8.13D Shapes4.8.2Surface Area4.8.3Volume4.8.4Exam-Style Questions - Volume
5

Vectors & Transformation Geometry

5.1

Vectors

5.1.1Vectors5.1.2Vectors 25.1.3Exam-Style Questions - Vectors
5.2

Transformation Geometry

5.2.1Transformations5.2.2Rotations5.2.3Translations & Reflections5.2.4Enlargements5.2.5Effects of Transformations
6

Statistics & Probability

6.1

Statistical Measures

6.1.1Basic Statistics6.1.2Frequency Table
6.2

Graphical Representation of Data

6.2.1Pictograms, Bar Charts & Pie Charts6.2.2Histograms6.2.3Cumulative Frequency6.2.4Cumulative Frequency 26.2.5Exam-Style Questions - Cumulative Frequency6.2.6End of Topic - Datasets
6.3

Probability

6.3.1Probability6.3.2Theoretical Probability6.3.3Experimental Probability6.3.4Venn Diagrams6.3.5Sample Space Diagrams6.3.6Tree Diagrams6.3.7Independent Events6.3.8Conditional Probability6.3.9End of Topic Test - Probability6.3.10Exam-Style Questions - Probability

Practice questions on Vectors 2

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

  1. 1
    What happens to a vector when it is multiplied by a scalar?Multiple choice
  2. 2
    What happens to a vector when it is multiplied by a negative scalar?Multiple choice
  3. 3
    What is the condition for A, B and C lying on a straight line?Multiple choice
  4. 4
    What is the condition for the points X, Y and Z lying on a straight line?Multiple choice
  5. 5
    How can you calculate the magnitude of a vector?Multiple choice
Answer all questions on Vectors 2

Unlock your full potential with Seneca Premium

  • Unlimited access to 10,000+ open-ended exam questions

  • Mini-mock exams based on your study history

  • Unlock 800+ premium courses & e-books

Get started with Seneca Premium

Vectors

Exam-Style Questions - Vectors