Karate Chop
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Hi, I'm having a few troubles with this question on my assignment. I've tried for many hours to get out the answer but i keep getting stuck and am not sure if I'm going about it the right way.
This is the question:
Three concurrent lines OA, OB and OC are produced to D, E and F respectively. Prove, using vectors, that the point of intersection of AB and DE, BC and EF, CA and FD are collinear.
What worked out the equations of the lines going through the points A and B, D and E, etc. and then made the equations of lines through A and B and D and E equal each other, since they were the position vectors of any point along that line. I did this inorder to try to get the points D, E and F in terms of a, b and c (the position vectors of A, B and C respectively), however in my last and most successful attempt at this question, i end up with 3 sets of two simultaneous equations, each set had three different variables so i couldn't solve it. Please help! thanks in advance. john.
This is the question:
Three concurrent lines OA, OB and OC are produced to D, E and F respectively. Prove, using vectors, that the point of intersection of AB and DE, BC and EF, CA and FD are collinear.
What worked out the equations of the lines going through the points A and B, D and E, etc. and then made the equations of lines through A and B and D and E equal each other, since they were the position vectors of any point along that line. I did this inorder to try to get the points D, E and F in terms of a, b and c (the position vectors of A, B and C respectively), however in my last and most successful attempt at this question, i end up with 3 sets of two simultaneous equations, each set had three different variables so i couldn't solve it. Please help! thanks in advance. john.