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Vectors

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Published in: Mathematics
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Vector Geometry

Divya J / Dubai

15 years of teaching experience

Qualification: CAIE and Pearson Examiner for IGCSE an AS Levels, Masters in Mathematics

Teaches: SAT, ACT, Maths, IGCSE/AS/AL, Physics, Biology, Chemistry, Mathematics

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  1. Subject - Mathematics Lecture No.- 07 Chapter • Vectors Today's Targets Vector Geometry
  2. Vector Geometry Vector methods can be used to solve geometric problems in two dimensions and produce simple geometric proofs.
  3. Question Tis the midpoint of the line PS and R divides the line QS in the ratio 1 : 3. PT = a and PQ = b (a) Express each of the following in terms of a and b: (i) PS (iii) PR (b) Show that RT = (2a - 3b).
  4. Question ABC is an isosceles triangle. L is the midpoint of BC. M divides the line LA in the ratio 1 : 5, and N divides AC in the ratio 2 : 5. (a) (b) BC = p and BA = q. Express the following in terms of p and q. (i) LA (ii) AN Show that MN — llp).
  5. [W19, 43, Q 11] ()AB is a triangle and ABC and PQC are straight lines. P is the midpoint of ()A. Q is the midpointof PC and OQ : QB = 3 : 1. OA = 4a and 0B = 8b. NOT TO SCAL AB = .... ..... OQ=.. Find, in terms of a and/or b, in its simplest form AB OQ (ii) (iii) [1]
  6. [W19, 43, Q 11] ()/IB is a triangle and ABC and PQC are straight lines. P is the midpoint of ()A. Q is the midpoint of PC and OQ : QB = 3 : 1. OA = 4a and 0B = 8b. NOT TO SCAL (b) By using vectors, find the ratio AB : BC.
  7. [W14, 22, Q 19] The diagram shows a quadrilateral OABC. OA = a, OC = c and CB = 2a X is a point on 0B such that 1 : 2. (a) Find, in terms of a and c, in its simplest form (i) AC [1] (ii) AX AX - ................. [3]
  8. [W14, 22, Q 19] The diagram shows a quadrilateral OABC. OA = a, OC = c and CB = 2a X is a point on 0B such that 1 : 2. (b) Explain why the vectors AC and AC show that C, X and A lie on a straight line.
  9. Revision Parallel vectors: Two vectors are parallel if and only if one is a multiple of the other. This tends to appear in vector proofs in the following ways: If you find in your workings that one vector is a multiple of the other, then you know that the two vectors are parallel - you can then use that fact in the rest of the proof. If you need to show that two vectors are parallel, then all you need to do is show that one of the vectors multiplied by some number is equal to the other one.
  10. Revision Points on a straight line: Often you are asked to show in a vector proof that three points lie on a straight line (i.e., that they are collinear). To show that three points A, B and C lie on a straight line: Show that the vectors connecting the three points are parallel. For example, show that AB is a multiple of (and therefore parallel to) AC, or that AB is a multiple of (and therefore parallel) to BC. As those two vectors are parallel and they share a common point it means that the three lines form a straight line.

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