# Math Help - 3d vector

1. ## 3d vector

Question: The position vectors of the points A, B and C referred to an origin O are 4i-3j-k and -8i+6j+5k respectively. If AB meets the z-axis at P, find the ratio AP:PB.

What is mean by "If AB meets the z-axis at P" ?
Can anyone explain to me please?
And how do I solve it?

2. ## Re: 3d vector

Originally Posted by alexander9408
Question: The position vectors of the points A, B and C referred to an origin O are 4i-3j-k and -8i+6j+5k respectively. If AB meets the z-axis at P, find the ratio AP:PB.

What is mean by "If AB meets the z-axis at P" ?
Can anyone explain to me please?
And how do I solve it?

1. Stationary vector of C ( $\vec c$) is missing.
$AB: r = \langle 4,-3,-1 \rangle + t \cdot \langle 12, -9 ,-6 \rangle$
If this line has a common point with the z-axis the point P has the coordinates $P(0,0,p)$
3. When you finally have found $P(0,0,1)$ calculate the distances $|\overline{AP}|$ and $|\overline{BP}|$ and determine the ratio of the distances. I've got $\frac{|\overline{AP}|}{|\overline{BP}|} = \frac12$