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- 1Recall the definition of a vector and identify vectors in component form notation
- 2Display three vector notations on the board: (3, 2), (−1, 4), and (0, 5). Ask learners: What do the two numbers inside the brackets tell us about each vector? Learners discuss with a partner, then a volunteer shares their answer
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- VECTOR ADDITION IN COMPONENT FORM
- 1Write two vectors on the board: vector **a** = (2, 3) and vector **b** = (1, −2). Explain that to add them, we add the first components together and the second components together: (2 + 1, 3 + (−2)) = (3, 1). Ask learners to repeat the rule aloud in unison three times. Work through a second example with vectors (−1, 4) and (2, 2) together as a class, writing each step on the board using the textbook's worked example on page 45 as a reference
- 2Distribute rulers and exercise books to each learner. Display vector **p** = (3, 2) and vector **q** = (−2, 1) on the board. Learners use their ruler and graph board to draw both vectors starting from the origin, then calculate **p** + **q** in their exercise books and write the answer as a component. Invite a learner who found this easy to show their vector diagram on the board while explaining each step
- 3Struggling learners: provide a partially completed worked example with blanks to fill in for the addition rule; fast finishers calculate the sum of three vectors instead of two.
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- 1Textbook
- 2Exercise book
- 3Ruler and graph board
- 4Calculator
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- 1Display the statement on the board: 'To add vectors (a, b) and (c, d), the answer is (a + c, b + d).' Learners show thumbs up if they agree, thumbs down if they disagree, then explain their choice to their partner
- 2Call on one representative from each pair of learners to state one rule or fact they learned about vector component form today
Exercise
- 1Given vector **m** = (5, −1) and vector **n** = (−3, 4), calculate **m** + **n** and write your answer in component form. Show your working in your exercise book
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- 1Recall the properties of equal vectors and identify when two vectors are equal
- 2Ask learners: What do you remember about equal vectors from yesterday's lesson? Learners whisper their answers to their partners, then one representative from each group shares one property aloud
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- APPLYING VECTOR EQUALITY TO SOLVE PROBLEMS
- 1Write this problem on the board: Kofi walks from Market point A to point B, covering 5 km north. Ama walks from point C to point D, covering 5 km north. Are vectors AB and CD equal? Using the ruler and graph board, ask learners to draw both vectors to scale on their exercise books. Ask: What is the same about both vectors? What does this tell us about equality? A volunteer comes to the board and explains that both vectors have the same magnitude (5 km) and direction (north), so they are equal
- 2Present this task: Two delivery trotros start from different markets in Accra. Trotro 1 travels from Makola Market to Kaneshie (8 km east, 3 km south). Trotro 2 travels from Madina Market to Tema (8 km east, 3 km south). Using your calculator and ruler, show whether these displacement vectors are equal. Learners work in pairs: they draw the vectors on graph board, measure the magnitudes using the ruler, and use the calculator to confirm if both vectors match in magnitude and direction. Pairs check each other's work and report which vectors are equal
- 3Struggling learners: work with one vector pair only and use the ruler to measure pre-drawn vectors. Fast finishers: create their own two-vector equality problem using two different Ghanaian locations and present the solution to a peer.
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- 1Textbook
- 2Exercise book
- 3Calculator
- 4Ruler and graph board
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- 1Ask learners: When we say two vectors are equal, what two things must be exactly the same? Learners respond chorally: magnitude and direction. Repeat three times for reinforcement
- 2Learners compare their vector drawings with the person sitting next to them and explain aloud to their partner why their two vectors are or are not equal
Exercise
- 1Abena drives a delivery van from Takoradi Market 12 km west and 5 km north to reach a shop. Kwesi cycles from Bolgatanga Market 12 km west and 5 km north to reach a store. Are the displacement vectors equal? Use your ruler and exercise book to draw both vectors and explain your answer in one sentence
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