Thread: 3D vector question

The position vectors of the points A and B relative to an origin O are 5i + 4j + k, -i + j - 2k respectively. Find the position vector of the point P which lies on AB produced such that AP=2BP.

My strategy was to calculate AB, then take 1/3 of this and add it to the position vector for B. However this returns the incorrect answer.

Any ideas?

Originally Posted by hymnseeker

My strategy was to calculate AB, then take 1/3 of this and add it to the position vector for B.

The equation that is B is between A&P.
Your approach puts P between A&B.
Try this . Does that work?

Hello, hymnseeker!

The position vectors of points and relative to an origin
are: .

Find the position vector of point which lies on produced so that:

My strategy was to calculate AB, then take 1/3 of this ... .no

Did you make a sketch?

Code:

      : ← - - - - 2 - - - - → :
      *-----------*-----------*
      A           B ← - 1 - → P

As you can see, is the midpoint of

I see...

Thanks for your help Plato and Soroban, I understand now.