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.

2. AB is a straight line passing through A and B:

$AB: r = \langle 4,-3,-1 \rangle + t \cdot \langle 12, -9 ,-6 \rangle$

If this line has a common point with the z-axis the point P has the coordinates $P(0,0,p)$

Determine 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 $\frac{|\overline{AP}|}{|\overline{BP}|} = \frac12$

3. ## Re: 3d vector

how to determine the p? pls hlp me.

4. ## Re: 3d vector

Originally Posted by almostSeeker
how to determine the p? pls hlp me.
Good morning,

take this equation:

AB: r = \langle 4,-3,-1 \rangle + t \cdot \langle 12, -9 ,-6 \rangle

and replace $\vec r = \langle x,y,z \rangle$

Since P has the coordinates $P(0,0,p)$ you'll get
$\begin{array}{lcr}0&=&4+12t \\ 0&=&-3-9t \\p&=&-1-6t\end{array}$

1. Use the 1st or the 2nd equation to determine t.
2. Sub in this value into the 3rd equation to get the value of p.

thanks sir