Algebra Some Current Trends by Avramov L.L. (ed.), Tchakerian K.B. (ed.)

By Avramov L.L. (ed.), Tchakerian K.B. (ed.)

Show description

Read or Download Algebra Some Current Trends PDF

Similar algebra books

Additional resources for Algebra Some Current Trends

Example text

6. Three non-coplanar vectors u, v, w are given. Referred to these vectors as base vectors, the vectors, e, f, g, h are given by: 1 1 2 —1 e= (0) , f= (1) , g = (3), h = 4 ( 1) . 0 1 3 0 Express e, f, g, h as column vectors taking v +w, w +u, u + v as base vectors. 7. Write down the coordinates of the mid-points of the lines joining the following pairs of points: (i) (2, 4), (4, 6); (ii) (-2, 4), (4, 2); (iii) (— 1, — 3), (2, —4); (iv) (3, 1, —5), (2, —4, 0); (v) (a + b, a, a — b), (a —b, —a, — a — b).

Prove that the position vector of L is c. CM . NB — +1, where the magnitude and sense of each line segment is taken into account. ) 11. If a transversal cuts the sides BC, CA, AB of a triangle ABC at L, M, N respectively, prove that BL. CM. AN _ —1 LC . NB magnitudes and senses of each line segment being taken into account. ) 12. ABCD is a plane quadrilateral. AB and DC meet at P; BC and AD meet at Q. Prove that the mid-points of AC, BD and PQ are collinear. 13. P, Q are variable points on two skew lines.

Why is it not possible to express CD in terms of the two vectors PQ, AR? 13. ABCDEF is a regular hexagon, and AB = a, BC = b. Find CD, DE, EF, FA in terms of a and b. 14. ABCDA'B'C'D' is a cuboid whose base ABCD is a square of side 2 units. , are vertical and of magnitude 4 units. E is the mid-point 31 VECTORS AND VECTOR GEOMETRY [2 of AB, G is the mid-point of B'C' and F is the mid-point of CC'. a, b, c are three vectors, each of magnitude 1 unit in the directions AB, AD, AA' respectively. Find, in terms of a, b, c the vectors DE, AF, EF, GF, GE.

Download PDF sample

Rated 4.89 of 5 – based on 40 votes