1 Vectors H070 Topic Title H470 Topic Title
2 Vectors Defining vectors Column notation Multiplication by scalarNegative vectors Addition of vectors Subtraction of vectors Problem solving
3 Q R P S PQ RS
4 Q R 4 a –4 5 b P 3 S = b = PQ RS = a =
5 Column notation The TOP number describes the HORIZONTAL movement.POSITIVE means RIGHT. NEGATIVE means LEFT. The BOTTOM number describes the VERTICAL movement. POSITIVE means UP. NEGATIVE means DOWN.
6 b b b b = 3b = ? 3b =
7 Vector multiplied by scalarIf we multiply a VECTOR by a scalar it’s the same as adding to that many times. 3b = b + b + b In column vector form we just have to multiply both the HORIZONTAL and VERTICAL components by the number.
8 a = a –a –a = If we take the negative of a vector it’s the same as just reversing the direction of the vector.
9 a a a a a I haven’t mentioned anything about an origin. The vector could be anywhere and still be the same.
10 b –b ½b 2a –2a a b a = b =
11 a = b = a b a + b a + b =
12 b + a a = a b b = b + a =
13 When adding two vectors in a diagram we place the second vector at the end of the first. In column notation this means we just add the HORIZONTAL and VERTICAL components. If we have 2 vectors a and b, it doesn’t matter which order we add them, we get the same RESULTANT vector. This is the COMMUTATIVE LAW. a + b = b + a
14 b = –b b a – b a a = a – b = a + (–b) =
15 Challenge You have a large supply of vectors a and b which are: a =Starting at the origin you take a 2 step walk where each step is either a or b or a scalar multiple of a or b. Define the vector expression from the origin to each of the corner positions on a –5 to 5 grid. Which coordinate points can you visit within the grid?
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