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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.

I appreciate your help.[/FONT]
 

Dr.Peterson

Active 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.

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'
 

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.

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

Thank you


 
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