Consider the points P = (1,2,0), Q = (0,1,2), and R=(2,0,1). Let A be an arbitrary point in 3-dimensional space. Draw a picture which shows that A lies on the line joining P and Q if and only if OÀ=OP+tPQ. for some value of t. If M is the midpoint of the line segment PQ, give values of a and b such that OM - GOP+ boo. =
Consider the points P = (1,2,0), Q = (0,1,2), and R=(2,0,1). Let A be an arbitrary point in 3-dimensional space. Draw a picture which shows that A lies on the line joining P and Q if and only if OÀ=OP+tPQ. for some value of t. If M is the midpoint of the line segment PQ, give values of a and b such that OM - GOP+ boo. =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Consider the points** \( P = (1, 2, 0) \), \( Q = (0, 1, 2) \), and \( R = (2, 0, 1) \).
Let \( A \) be an arbitrary point in 3-dimensional space. Draw a picture which shows that \( A \) lies on the line joining \( P \) and \( Q \) if and only if
\[
\overrightarrow{OA} = \overrightarrow{OP} + t \overrightarrow{PQ}
\]
for some value of \( t \).
If \( M \) is the midpoint of the line segment \( \overline{PQ} \), give values of \( a \) and \( b \) such that
\[
\overrightarrow{OM} = a \overrightarrow{OP} + b \overrightarrow{OQ}.
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ef06bb3-2d9b-4f27-bb3b-835b443ab608%2F44627832-8444-488b-8adc-d49268c43c8a%2Fl4shbh2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Consider the points** \( P = (1, 2, 0) \), \( Q = (0, 1, 2) \), and \( R = (2, 0, 1) \).
Let \( A \) be an arbitrary point in 3-dimensional space. Draw a picture which shows that \( A \) lies on the line joining \( P \) and \( Q \) if and only if
\[
\overrightarrow{OA} = \overrightarrow{OP} + t \overrightarrow{PQ}
\]
for some value of \( t \).
If \( M \) is the midpoint of the line segment \( \overline{PQ} \), give values of \( a \) and \( b \) such that
\[
\overrightarrow{OM} = a \overrightarrow{OP} + b \overrightarrow{OQ}.
\]
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