2 STARTER – VECTOR SHAPES AIM: UNDERSTAND VECTOR NOTATION242-4-41)The shape is an isosceles triangle2)325-3-2-5The shape is a parallelogram3)-2-46-14-3The shape is a trapeziumTry adding the vectors in each question. What answer do you get each time?
3 STARTER – VECTOR SHAPES AIM: UNDERSTAND VECTOR NOTATIONWrite the vectors to draw a:-1)Rectangle2)Kite3)Right-angled triangle4)RhombusAdd up your vectors each time and make sure that your totals are correct.
4 VECTOR SHAPES-MULTIPLY BY A SCALAR Write the vectors to draw a:-1)Rectangle2)Now redraw your rectangle, enlargement scale factor 2, and write down your vectors3)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.
5 RESULTANT VECTORS – FIND THE SHORTEST JOURNEY 1)Draw a diagram to show the following journey.231-5AB =BC =2)Now join up A to C and find the vectorAC =3-2
6 RESULTANT VECTORS – FIND THE SHORTEST JOURNEY 133-1421)AB =BC =AC =54542)AB =BC =AC =-245-2323)AB =BC =AC =Can you find a quicker way of finding the resultant vector than drawing the diagram?
7 MAIN – VECTORS IN GEOMETRY Vectors show magnitude (length) and directionThe symbol for a vector is a bold letterVectors on a coordinate grid are shown by a column vectorVectors 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 vectorsA negative sign reverses the direction of the vector
8 MAIN – VECTORS IN GEOMETRY BCDEFGHIJKLMNOPQRSTUVWXNO =aOI =bbaFind the vectors for:-NP =2aDE =aPN =-2aXU =-3aOC =2bXF =3bAM =-2bDV =-3bNI =a + bIN =-a-bPF =2a + 2b
9 MAIN – VECTORS IN GEOMETRY AIM:Write vectors in terms of a,b or a and bADCBa2ab-aBA =AB+BCAC == a + bDC+CBDB == 2a - bAC+CDAD =AD =AB +BC +CD= a + b – 2a= a + b –2a= -a + b or b - a= -a + b or b - a
10 MAIN – VECTORS IN GEOMETRY AIM:Write vectors in terms of a,b or a and bLKMCBAbaK,L and M are mid-points of AB,BC and CA respectivelyAB =2aCA =-2bBC =BA +AC= -2a + 2b= 2b – 2aBL =½ BC= b – aWhat does this mean about KL and AC?KL =KB +BL= a + b – a= b