www mathsrevision com Nat 5 Vectors and Scalars

www. mathsrevision. com Nat 5 Vectors and Scalars Adding / Sub of vectors Position Vector Magnitude of a Vector Journeys 3 D Vectors Exam Type Questions www. mathsrevision. com

Vectors & Scalars www. mathsrevision. com Nat 5 A vector is a quantity with BOTH magnitude (length) and direction. Examples : Gravity Velocity Force

Vectors & Scalars www. mathsrevision. com Nat 5 A scalar is a quantity that has magnitude ONLY. Examples : Time Speed Mass

Vectors & Scalars www. mathsrevision. com Nat 5 A vector is named using the letters at the end of the directed line segment or using a lowercase bold / underlined letter u u This vector is named or u

Vectors & Scalars Also known as column vector Nat 5 www. mathsrevision. com A vector may also be represented in component form. w z

Equal Vectors www. mathsrevision. com Nat 5 Vectors are equal only if they both have the same magnitude ( length ) and direction.

Equal Vectors Nat 5 www. mathsrevision. com Which vectors are equal. a b c d g e f h

Equal Vectors Nat 5 www. mathsrevision. com Sketch the vectors 2 a , -b and 2 a - b a b -b 2 a

Vectors www. mathsrevision. com Nat 5 27 -Nov-20 Now try N 5 TJ Ex 15. 1 Ch 15 (page 143) Created by Mr. Lafferty@mathsrevision. com

Addition of Vectors Nat 5 www. mathsrevision. com Any two vectors can be added in this way b Arrows must be nose to tail a a+b

Addition of Vectors Nat 5 www. mathsrevision. com Addition of vectors B A C

Addition of Vectors Nat 5 www. mathsrevision. com In general we have For vectors u and v

Zero Vector Nat 5 www. mathsrevision. com The zero vector

Subtracting vectors Subtraction of Vectors Nat 5 think adding a negative vector www. mathsrevision. com u + (-v) Notice arrows nose to tail u u + (-v) = u - v -v v

Subtraction of Vectors Nat 5 www. mathsrevision. com Subtraction of vectors a a-b b

Subtraction of Vectors Nat 5 www. mathsrevision. com In general we have For vectors u and v

Vectors www. mathsrevision. com Nat 5 27 -Nov-20 Now try N 5 TJ Ex 15. 2 Ch 15 (page 145) Created by Mr. Lafferty@mathsrevision. com

A Position Vectors B www. mathsrevision. com Nat 5 A is the point (3, 4) and B is the point (5, 2). Write down the components of Answers the same !

A Position Vectors a Nat 5 www. mathsrevision. com 0 B b

A Position Vectors a Nat 5 www. mathsrevision. com 0 B b

Position Vectors www. mathsrevision. com Nat 5 If P and Q have coordinates (4, 8) and (2, 3) respectively, find the components of

Position Vectors www. mathsrevision. com Nat 5 P Graphically P (4, 8) Q (2, 3) p q-p Q q O

Position Vectors www. mathsrevision. com Nat 5 27 -Nov-20 Now try N 5 TJ Ex 15. 3 Ch 15 (page 146) Created by Mr. Lafferty@mathsrevision. com

Magnitude of a Vector www. mathsrevision. com Nat 5 A vector’s magnitude (length) is represented by A vector’s magnitude is calculated using Pythagoras Theorem. u

Magnitude of a Vector Nat 5 www. mathsrevision. com Calculate the magnitude of the vector. w

Magnitude of a Vector Nat 5 www. mathsrevision. com Calculate the magnitude of the vector.

Position Vectors www. mathsrevision. com Nat 5 27 -Nov-20 Now try N 5 TJ Ex 15. 4 Ch 15 (page 147) Created by Mr. Lafferty@mathsrevision. com

Vector Journeys Nat 5 www. mathsrevision. com As far as the vector is concerned, only the 27 -Nov-20 FINISHING POINT in relation to the STARTING POINT is important. The route you take is IRRELEVANT. Created by Mr. Lafferty@mathsrevision. com

Vector Journeys www. mathsrevision. com Nat 5 27 -Nov-20 Z Y M W Given that X u find Created by Mr. Lafferty@mathsrevision. com v

Vector Journeys www. mathsrevision. com Nat 5 27 -Nov-20 2 u Z Y M W u Created by Mr. Lafferty@mathsrevision. com X v

Vector Journeys www. mathsrevision. com Nat 5 27 -Nov-20 Now try N 5 TJ Ex 15. 5 Ch 15 (page 149) Created by Mr. Lafferty@mathsrevision. com

3 D Coordinates www. mathsrevision. com Nat 5 In the real world points in space can be located using a 3 D coordinate system. For example, air traffic controllers find the location a plane by its height and grid reference. z y O (x, y, z) x

3 D Coordinates Nat 5 www. mathsrevision. com Write down the coordinates for the 7 vertices z (0, 0, 2) F (0, 0, 0) G E(0, 1, 2) H O y (6, 0, 2)B 6 A(6, 1, 2) 2 1 D(6, 1, 0) C (6, 0, 0) What is the coordinates of the vertex H so that it makes a cuboid shape. x H(0, 1, 0 )

3 D Vectors www. mathsrevision. com Nat 5 Good News All the rules for 2 D vectors apply in the same way for 3 D.

Addition of Vectors Nat 5 www. mathsrevision. com Addition of vectors

Addition of Vectors Nat 5 www. mathsrevision. com In general we have For vectors u and v

Magnitude of a Vector www. mathsrevision. com Nat 5 A vector’s magnitude (length) is represented by A 3 D vector’s magnitude is calculated using Pythagoras Theorem twice. z v y 1 2 O 3 x

Subtraction of Vectors Nat 5 www. mathsrevision. com Subtraction of vectors

Subtraction of Vectors Nat 5 www. mathsrevision. com For vectors u and v

Position Vectors www. mathsrevision. com Nat 5 A (3, 2, 1) z a y 1 2 O 3 x

Position Vectors www. mathsrevision. com Nat 5

3 D Vectors www. mathsrevision. com Nat 5 27 -Nov-20 Now try N 5 TJ Ex 15. 7 Ch 15 (page 150) Created by Mr. Lafferty@mathsrevision. com

Are you on Target ! www. mathsrevision. com Nat 5 • Update you log book • Make sure you complete and correct ALL of the Vector questions in the past paper booklet.