MTH2: VECTOR GEOMETRY

This unit is about vector geometry which should help you to think geometrically.

VECTOR GEOMETRY

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  1. In the parallelogram OAB, A is (-1,7) and C is (-3, -3) . Find the coordinates of B.

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  1. In the parallelogram OPQR, P is (5, 8) and Q is (7, 4) Find the coordinates of R.

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In the figure, x divide OA in the ratio 2: 1, y is the mid point of OB. If OXYP is parallelogram,

Find;-

  1. The column vector for XY
  2. The coordinates of P

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  1. P is (-9, 3) and Q is (5, 10) S and 7 . Find the column vector for PS. Hence find the coordinates of S.
  2. OCDE is a parallelogram. C is (7,6) and D is (16, 8).
  3. find the coordinates of E
  1. calculate the lengths and .
  2. What can you deduce about OCDE?

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A VIDEO EXPLAINING ABOUT VECTORS

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  1. The origin , for the porposes of this question, is at the tip of my nose. Afly is sitting there and when I brush it away its motion is given by the vectors;

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Where is the fly . After these four moves , assuming that I still?

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  1. How far from the origin are the points A(3,4,12) and B (-1,-4,8)

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Parallel Vectors.

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Collinear points

AB and C colline or if they lie on the same straight line.

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AB Parallel        BC

But AB and BC share the common point B there fore A, B and C are collinear.

Exercise D.

  1. A (2,-2) ,B is (8,10) and C is (12, 18)
  2. Find the colunm vectors for AB and BC

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  1. Using column vectors, show that OMQN is parallelgram.
  2. A quadrilatral has vertices D(-1, -2) E(-3, 2) F(3, 4) and G(5, -2).
  3. P, Q, R and S are mid points of , ,

A VIDEO ABOUT VECTORS


What are their coordinates?

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  1. What is the relation between the diagonals of the quadrilaterals and the sides of the parallelogram.

Futher vectors

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Exercise:
In the figure , εC=C and Dε=D,εB=Dε andAε=2εC
By expressing AB and DC in terms of C and D, show that AB and DC are pallel.
AB = Aϵ + ϵB

2C+2d
2(c+d)
DC=Dε+ εC
=d+c
AB=2DC
⟹ABII DC

What is the relation between the lengths (AB) ̅ and (DC) ̅?

AB =2∆C

In the figure S, Y and Z are oints of the sides of the triangle PQR and PZ = Z and YP = Y.

  1. Show that corresponding sides of he triangle PZY, ZOX and YXP represent equal vectors. Are the riangle congruent.

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  1. The diagram below shows a quadrilateral OSRQ . OS = q , OP = p and SX = K (SP)
  1. Express vectors SP and OX interms of P, Q and K.

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  1. In figure above OA = a, OB = b, F nad G are points on AC such that AF : AB = 3:4 and AG : Ac = 2:3 respectively.
  2. Express AG and AC interms of AB hence find in terms of a vector a and b the vector AB : AC : DG and OF
  3. Determine the ratio DG : OC

 

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ASSIGNMENT : VECTOR GEOMETRY ASSIGNMENT MARKS : 20  DURATION : 60 minutes

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