# Thread: Pre-U Vector Question: Line has equation r = 9i − j + 8k + λ(3i − j + 2k)

1. ## Pre-U Vector Question: Line has equation r = 9i − j + 8k + λ(3i − j + 2k)

Hello,

I'm having trouble answering this question.

Q: Relative to the origin O, the point A has position vector given by OA = i + 2j + 4k. The line lhas

r = 9i j + 8k + 3i j + 2k.Find the position vector of the foot of the perpendicular from A to l. Hence find the position

vector of the reflection of A in l.

I found the position vector of the foot of the perpendicular as 3/2i + 3/2j + 3k.
But I don't understand how to answer the second part.

I appreciate your help.

2. Originally Posted by Yoshimineb
Hello,

I'm having trouble answering this question.

Q: Relative to the origin O, the point A has position vector given by OA = i + 2j + 4k. The line l has r = 9i j + 8k + 3i j + 2k. Find the position vector of the foot of the perpendicular from A to l. Hence find the position vector of the reflection of A in l.

I found the position vector of the foot of the perpendicular as 3/2i + 3/2j + 3k.
But I don't understand how to answer the second part.

I appreciate your help.
You seem to have omitted the variable on the right side of the equation of the line.

But the reflection can be found by going as far beyond the line as you have gone to the foot of the perpendicular. That is, just add to OA twice the vector from A to the foot:

A--------->F--------->A'

3. Originally Posted by Dr.Peterson
You seem to have omitted the variable on the right side of the equation of the line.

But the reflection can be found by going as far beyond the line as you have gone to the foot of the perpendicular. That is, just add to OA twice the vector from A to the foot:

A--------->F--------->A'
Hello Dr.Peterson,

I'm sorry for my carelessness. r = 9i j + 8k + λ(3i j + 2k) is the equation of the line.

From your help, I got the answer using OA + 2AF.

Thank you

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