Consider the ragular hexagon ABCDEF with centre at O (origin). Solution 2. Let ABCDEF be regular hexagon.Then $\\overline{AB} +\\overline{AC}+\\overline{AD}+\\overline{EA}+\\overline{FA} =?$ my answer is $3\\overline{AB}$ but â¦ Show that the points whose position vectors are â2 a + 3 b + 5 c, a + 2 b + 3 c, 7 a â c are collinear when a, b, c are non - coplanar vectors. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Vector and 3-D Geometry : Course in Mathematics for the IIT-JEE and Other Engineering Entrance Examinations Choubey K. R. All the solutions of Construction of Polygons (Using ruler and compass only) - Mathematics explained in detail by experts to â¦ Let a = 2 i + 4 j â5 k, b = i + j + k and c = j + 2 k. Find unit vector in the oppo-site direction of a + b + c. 7. Show that c b + c + 2a b c a c + a + 2b = 2(a + b + c)3. All sides are equal, all angles are equal. Now, note that BE bisects the angle at B. Let ABCbe a triangle with sides a, b, c, inradius rand circumradius R(using the conventional notation). To describe this structure consider a two-dimensional array of equilater triangles (or regular hexagons including their centers) of edge a, as indicated in Fig. (a) No. 22. Express 2 a-3 b in terms of u and v, and simplify, when a = u + v, b = 3 u-2 v. 12. 3AD = AB + AC + AD + AE + AF => 2AD = AB + AC + AE + AF. given AB =a BC =b here a and b are vector EF=-b DE=-a and we know that AD=2BC =2b AD=AB+BC+CD 21. 3. RD Sharma solutions for Class 12 Maths chapter 23 (Algebra of Vectors) include all questions with solution and detail explanation. Since it's a regular hexagon, AB = AF, and by symmetry, AC = AE, so . Then their resultant is This preview shows page 3 - 4 out of 4 pages.. 11. Let R be the resultant vector making an angle Î¸ with AX and at a distance d from the center of hexagon. 12 Let ABCDEF be a regular hexagon and put a AB b BC Find vector expressions in from MATH 1002 at The University of Sydney We have step-by-step solutions for your textbooks written by Bartleby experts! Question 10. The measure of each interior angle of a regular polygon of n (n - 2)180 sides is Theorem 117. Prove that if a completely symmetric set is finite, then it consists of the vertices of either a regular polygon, a regular tetrahedron, or a regular octahedron. As, AD = 2BC {Properties of a regular hexagon, also AD || BC (Parallel)} Putting in equation (i), Option(C)is the answer. A concave polygon is a polygon in which atleast one interior angle is more than 180°. Let ABCDEF be a regular hexagon.If AD=xBC and CF=yAB, then xy= ? Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share â¦ The diagonals AD, BE, CF intersect and each diagonal does bisect the area. If their resultant passes through C on AB, then A. Thus AE^2 = 5^2+6^2-(2*5*6)/2. AD^2 = AC^2+CD^2, Angle ACD being 90 deg. Regular hexagons have six equal sides and angles and are composed of six equilateral triangles. Find the number of sides of a regular polygon if each of its interior angle is 168°. A quadrilateral in which at least one set of opposite sides is parallel is known as trapezium or trapezoid.The non-parallel sides if any (AD and BC in the given figure) are known as oblique sides.If length of oblique sides is equal, it is known as isosceles trapezium.Parallel sides (AB and DC) are generally known as bases and the perpendicular distance between bases is known as height. The measure of each exterior angle of a regular polygon of n