Vector Perpendicular: Finding Point P from A & B

[thomas49th]

Homework Statement

The equation for the line that goes through vector points A and B is

i - 5j - 7k + t(9i + 15j + 12k)

A is defined: i - 5j - 7k
B is defined: 10i + 10j + 5k

Find the position vector of point P such that OP is perpendicular to AB

The Attempt at a Solution

well a.b = 0 to be perpendicular

but how does that help...

Im lost

Any ideas. My test is at 9am tomorrow (GMT). Can someone just explain the whole method for me.


Thanks

 

[rootX]

(9i + 15j + 12k) is your direction vector

so you need <a,b,c> direction vector such that
<a,b,c> . (9, 15, 12,) = 0

pick any values for a,b,c

so the line perpendicular is r = (0,0,0) + t <a,b,c>

now, find intersection

 

[tiny-tim]

The equation for the line that goes through vector points A and B is

i - 5j - 7k + t(9i + 15j + 12k)

A is defined: i - 5j - 7k
B is defined: 10i + 10j + 5k

Find the position vector of point P such that OP is perpendicular to AB

well a.b = 0 to be perpendicular

Hi thomas49th!

(btw, B isn't 10i + 10j + 5k, is it? )

I assume P is to be on AB?

ok, then OP must be i - 5j - 7k + t(9i + 15j + 12k)
for some value of t.

And, as you say, AB.OP = 0.

So … ?

I got to go to bed now … :zzz: