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

#### Yoshimineb

##### New member
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 l has

equation 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 3/2[FONT=&quot]i [/FONT]+ 3/2[FONT=&quot]j [/FONT]+ 3[FONT=&quot]k.
But I don't understand how to answer the second part.

#### Dr.Peterson

##### Elite Member
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 equation 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.

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'

#### Yoshimineb

##### New member
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.