VECTORS IN GEOMETRY

STARTER – VECTOR SHAPES AIM: UNDERSTAND VECTOR NOTATION 2 4 2 -4 -4 1) The shape is an isosceles triangle 2) 3 2 5 -3 -2 -5 The shape is a parallelogram 3) -2 -4 6 -1 4 -3 The shape is a trapezium Try adding the vectors in each question. What answer do you get each time?

STARTER – VECTOR SHAPES AIM: UNDERSTAND VECTOR NOTATION Write the vectors to draw a:- 1) Rectangle 2) Kite 3) Right-angled triangle 4) Rhombus Add up your vectors each time and make sure that your totals are correct.

VECTOR SHAPES-MULTIPLY BY A SCALAR Write the vectors to draw a:- 1) Rectangle 2) Now redraw your rectangle, enlargement scale factor 2, and write down your vectors 3) Compare your vectors from question 1 and question 2. What do you notice? 4) Repeat the above drawing a kite and then enlarging it scale factor 3.

RESULTANT VECTORS – FIND THE SHORTEST JOURNEY 1) Draw a diagram to show the following journey. 2 3 1 -5 AB = BC = 2) Now join up A to C and find the vector AC = 3 -2

RESULTANT VECTORS – FIND THE SHORTEST JOURNEY 1 3 3 -1 4 2 1) AB = BC = AC = 5 4 5 4 2) AB = BC = AC = -2 4 5 -2 3 2 3) AB = BC = AC = Can you find a quicker way of finding the resultant vector than drawing the diagram?

MAIN – VECTORS IN GEOMETRY Vectors show magnitude (length) and direction The symbol for a vector is a bold letter Vectors on a coordinate grid are shown by a column vector Vectors are equal if they have the same length and the same direction. The position of the vector on the grid does not matter. Equal vectors have identical column vectors A negative sign reverses the direction of the vector

MAIN – VECTORS IN GEOMETRY B C D E F G H I J K L M N O P Q R S T U V W X NO = a OI = b b a Find the vectors for:- NP = 2a DE = a PN = -2a XU = -3a OC = 2b XF = 3b AM = -2b DV = -3b NI = a + b IN = -a-b PF = 2a + 2b

MAIN – VECTORS IN GEOMETRY AIM:Write vectors in terms of a,b or a and b A D C B a 2a b -a BA = AB + BC AC = = a + b DC + CB DB = = 2a - b AC + CD AD = AD = AB + BC + CD = a + b – 2a = a + b –2a = -a + b or b - a = -a + b or b - a

MAIN – VECTORS IN GEOMETRY AIM:Write vectors in terms of a,b or a and b L K M C B A b a K,L and M are mid-points of AB,BC and CA respectively AB = 2a CA = -2b BC = BA + AC = -2a + 2b = 2b – 2a BL = ½ BC = b – a What does this mean about KL and AC? KL = KB + BL = a + b – a = b