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In ΔABC, D, E and F are the midpoint of AB, BC and CA respectively. BF and CD intersect at point O. Let vector AB=a and vector AC=b. Prove that AOE three points are on the same straight line, and AO: OE=BO: OF=CO: OD=2 Supplement to question: the answer is AE =1/2(a+b), so AO =(2/3) AE AO =(2/3) AE, how is this obtained?
It's very simple to pull, cross point B to make CE parallel line, and AO extension line at point M, cross point a to make AD parallel line intersection AD extension line at n, because d is the midpoint of ad, so o is the midpoint of am, so do is equal to 1/2bm, in the same way, an is equal to 2do, in the triangle anf and triangle CFO, af is equal to cf, and an is parallel to cd, so an is equal to co, so equal to bm, so e is the midpoint of cb. Mobile phone typing is too troublesome, see me so hard to remember to choose my best answer, hey hey
In triangle ABC, D, E, F are the midpoint of AB, BA, CA, respectively, BF and CD intersect at point O, let vector AB = vector a, vector AC = vector b 1. Prove that A, O and E are on the same straight line, and AO/OE=BO/OF=CO/OD=2 2. Use vectors a and b to represent vector AO In triangle ABC, D, E, F are the midpoint of AB, BA, CA respectively, BF and CD intersect at point O, let vector AB = vector a, vector AC = vector b 1. Prove that A, O and E are on the same straight line, and AO/OE=BO/OF=CO/OD=2 2. Use vectors a and b to represent vector AO In triangle ABC, D, E, F are the midpoint of AB, BA, CA, respectively, BF and CD intersect at point O, let vector AB = vector a, vector AC = vector b 1. Prove that A, O and E are on the same straight line, and AO/OE=BO/OF=CO/OD=2 2. Represent vector AO with vectors a and b
1. I'm sorry, I forgot half of the first question
2.|AO|=2/3AE
|AE|=1/2|a+b|
So |AO|=2/3x1/2|a+b|=1/3|a+b|
△ In ABC, D, E, F, is the midpoint of AB, BC, CA, prove: vector AE + vector CD + vector BF = vector 0
Since d, e, f are that midpoint of each side,
Therefore AE+CD+BF=1/2*(AB+AC)+1/2*(CA+CB)+1/2*(BA+BC)
=1/2*(AB+AC+CA+CB+BA+BC)
=0 .
Given A (1,1) B (3,-1) C (4,3)(1) If A, B and C are collinear, find the relation between a and b (2) If the vector of AC is equal to the vector of AB, find the coordinate of point C. The coordinates of point c are (a, b) not (4,3) Given A (1,1) B (3,-1) C (4,3)(1) If A, B, C are collinear, find the relationship between a and b (2) If the vector of AC is equal to the vector of AB, find the coordinate of point C. The coordinates of point c are (a, b) not (4,3)
A (1,1) B (3,-1) C (4,3)(1),(-1-1)/(3-1)=-1=(3+1)/(4-3)=4, so A, B and C are not collinear. Is your question wrong?
Given A (1,1) B (3,-1) C (a, b) If ABC is three collinear, find the relation of ab
0
Given A (1,1) B (3,-1) C (a, b)1. If ABC is a three-point collinear solution ab 2. If vector AC=2 vector AB find point C
0
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