# MTH2: VECTOR GEOMETRY

VECTOR GEOMETRY

##    1. In the parallelogram OAB, A is (-1,7) and C is (-3, -3) . Find the coordinates of B. 1. In the parallelogram OPQR, P is (5, 8) and Q is (7, 4) Find the coordinates of R.  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   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? A VIDEO EXPLAINING ABOUT VECTORS mvellal     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; Where is the fly . After these four moves , assuming that I still? 1. How far from the origin are the points A(3,4,12) and B (-1,-4,8) Parallel Vectors.    Collinear points

AB and C colline or if they lie on the same straight line.  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      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?    1. What is the relation between the diagonals of the quadrilaterals and the sides of the parallelogram.

Futher vectors  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.            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.    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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