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Maths revision course by Miriam Hanks 1 Vectors what are they? Vectors describe movements i, j and k represent movement in the x,y and z directions Slide 2 Maths revision course by Miriam Hanks 2 Vectors How to calculate To calculate vector BA, subtract: BA = a - b B O A Slide 3 Maths revision course by Miriam Hanks 3 resultant Vectors - resultants To find the resultant, add the components of the vectors together Slide 4 Maths revision course by Miriam Hanks 4 Vectors - magnitude The magnitude of a vector is its length. The notation for this is vertical lines: eg |a| or |PQ| To find the magnitude of a vector, use Pythagoras or the distance formula. Slide 5 Maths revision course by Miriam Hanks 5 Vectors - Collinearity To show that 3 points are in a straight line (ie collinear): Work out 2 vectors and show that one is a multiple of the other Show that the vectors have a common point Slide 6 Maths revision course by Miriam Hanks 6 Vectors in real life Sat navs work out their position from satellites in the sky, but then use vectors to decide on a route. Slide 7 Maths revision course by Miriam Hanks 7 Vectors Dot product There are 2 formulae for the dot product on the formula sheet: dot product = x 1 x 2 + y 1 y 2 +z 1 z 2 where x,y,z are the components of each vector. dot product = a b cos where a is the magnitude of vector a (use Pythagoras for this) Note these 2 formulae equal each other, so: a b cos = x 1 x 2 + y 1 y 2 +z 1 z 2 Slide 8 Maths revision course by Miriam Hanks 8 Dot product of vectors at 90 o The dot product of 2 vectors at 90 o is zero and vice versa Why? Slide 9 Maths revision course by Miriam Hanks 9 Dot product of a vector with itself The dot product of vector a with itself is: a2a2 Why? Slide 10 Maths revision course by Miriam Hanks 10 The dot product in real life When is the dot product used in real life? Computer games programmers use the dot product to find the angle between 2 characters, so they know whether they are facing each other.