Math Is Fun Forum

jimi70

Member

Registered: 2012-04-04

Posts: 22

triangle with vectors

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In the diagram, vector OB = b, vector OC = 4b/3 and vector AP = 2/3 vector AB.
Given that vector AQ = m vector AC and that vector OQ = n vector OP, calculate the values of m and n, and the ratio of the vectors AQ:QC.
I can't see how to use the vectors given only and I can't see any similar triangles. Can somebody get me started?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,164

Re: triangle with vectors

hi jimi70,

In 2D, if you have two vectors, not parallel, you can always write any other vector as a linear combination of those two vectors.

You have b as one such;  I suggest you use OA = a as the other.

A linear combination will look like this:

So write everything in terms of a and b.

So now we have two expressions for OQ.  They must be equal.  In fact, their a components must be equal and similarly the b components.

So you can form a pair of simultaneous equations in m and n and solve.

and

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

jimi70

Member

Registered: 2012-04-04

Posts: 22

Re: triangle with vectors

thanks again bob, I got all of that. Just one question: was there any particular reason why you chose a as the other vector?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,164

Re: triangle with vectors

No.  Any vector not parallel to b would do.

But a made it seem neat.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob