Question: 5. The points D, E and F divide the sides BC, CA and AB of a triangle in the ratios 1:4, 3:2 and 3

5. The points D, E and F divide the sides BC, CA

5. The points D, E and F divide the sides BC, CA and AB of a triangle in the ratios 1:4, 3:2 and 3 : 7 respectively. Show that there exists a point G such that the sum of the vectors AD, BE, CF is parallel to CG. What ratio does G divide AB? 6. ABCD is a plane quadrilateral and E is any point on AD. EF is drawn parallel to DB to meet AB in F, and EG is drawn parallel to DC to meet AC in G. Prove that FG is parallel to Bc. 7. G and G are the centroids of the two triangles ABC and A'BC'. Show that AA' + BB' + CC' = 3GG'. 8. ABCD is a trapezium such that DC = 3AB. If L and M are the midpoints of AD and BC respectively, Show that LM = 2AB. 9. The points D, E and F divide the sides BC, CA and AB of a triangle in the ratio 1:4, 3:2 and 3:7 respectively. Show that there exists a point G such that the sum of the vectors AD, BE, CF is parallel to CG. What is the ratio in which G divides AB?

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