Vectors Q--help much appreciated!

fernni SG

Sorry I can't figure out how to post image from iPad!

Here is the question. In a triangle ABC, Vector AB= 3a, AC= 4b, and BD = 2DC. E is the midpoint of AD and CE is produced to meet AB at point F. Find AF/AB.

I have thought for hours

wee_ws SG

Hi,

I presume this is pitched at H2 Maths level.

1. Let AF = mAB, so we could write m on AF and 1 - m on FB. Find the vector AF.

2. Find the vectors AD (by ratio theorem) and AE (half of AD).

3. Let EF = nCF. Find the vector CF (which is CA + AF).

4. Consider the vector equation AE + EF = AF, solve for m & n by comparisons.

Thanks.

Cheers,
Wen Shih

fernni SG

Thank you Wen Shih! Sorry for not stating clearly, this is an O lvl question from Commonwealth sec (last yr paper) worth 2 marks. Is there any alternative way to do the question?

wee_ws SG

Hi,

I do not feel that it is a straightforward question to worth only 2 marks (I could use this exact question and give it to my A-level students who may get stumped by it as well). Sometimes, teachers may set a tough question and allocate little marks because they do not want to penalise students too much (knowing students cannot manage this topic in the first place). Be comforted by the fact that Cambridge questions are more reasonable as there is tendency for it to provide guidance (via part questions) to lead you to the ratio.

Do not worry too much and revise your topics more comprehensively rather than spend much time on a single question, jiayou!

Cheers,
Wen Shih