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Understand Vector Geometry: Shapes & Journeys

Learn vector notation through isosceles triangles, parallelograms, trapeziums & shape transformations, finding shortest journeys and resultant vectors in geometry.

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Understand Vector Geometry: Shapes & Journeys

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  1. VECTORS IN GEOMETRY

  2. 5 0 -3 -2 3 2 -2 -4 6 0 -5 0 2 -4 2 4 -1 4 -3 0 -4 0 STARTER – VECTOR SHAPES AIM: UNDERSTAND VECTOR NOTATION The shape is an isosceles triangle 1) 2) The shape is a parallelogram 3) The shape is a trapezium Try adding the vectors in each question. What answer do you get each time?

  3. STARTER – VECTOR SHAPES AIM: UNDERSTAND VECTOR NOTATION Write the vectors to draw a:- 1) Rectangle 2) Kite 3) Right-angled triangle Rhombus 4) Add 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) Rectangle 2) Now redraw your rectangle, enlargement scale factor 2, and write down your vectors Compare your vectors from question 1 and question 2. What do you notice? 3) Repeat the above drawing a kite and then enlarging it scale factor 3. 4)

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

  6. BC = AB = AC = AB = AC = AC = BC = AB = BC = 3 -1 3 2 5 4 0 4 1 3 5 0 -2 4 4 2 5 -2 RESULTANT VECTORS – FIND THE SHORTEST JOURNEY 1) 2) 3) 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 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

  8. AM = NO = PF = IN = OI = NI = DV = XF = NP = DE = PN = XU = OC = MAIN – VECTORS IN GEOMETRY a b b a Find the vectors for:- -2a -3a 2a a 2b 3b -3b -2b a + b -a-b 2a + 2b

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

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

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