Finding a vector position
$begingroup$
"The position vectors of points $A$ and $B$ relative to the origin are
$3i+2j-k$ and $5i+6j+5k$ respectively. Find the position vector of the
point $P$ which lies on $AB$ produced such that $AP=3BP$."
Actually I can solve this, provided I find where P lies - on $AB$ line sector or the continuation of $AB$. That's exactly what I don't understand - how to visualize the problem.
How do I figure out where exactly $P$ lies?
geometry vectors
edited Dec 10 '18 at 6:56
Ali
1,9732520
asked Dec 8 '18 at 9:02
Windy Windy
31
$endgroup$
add a comment |
$begingroup$
"The position vectors of points $A$ and $B$ relative to the origin are
$3i+2j-k$ and $5i+6j+5k$ respectively. Find the position vector of the
point $P$ which lies on $AB$ produced such that $AP=3BP$."
Actually I can solve this, provided I find where P lies - on $AB$ line sector or the continuation of $AB$. That's exactly what I don't understand - how to visualize the problem.
How do I figure out where exactly $P$ lies?
geometry vectors
edited Dec 10 '18 at 6:56
Ali
1,9732520
asked Dec 8 '18 at 9:02
Windy Windy
31
$endgroup$
add a comment |
$begingroup$
"The position vectors of points $A$ and $B$ relative to the origin are
$3i+2j-k$ and $5i+6j+5k$ respectively. Find the position vector of the
point $P$ which lies on $AB$ produced such that $AP=3BP$."
Actually I can solve this, provided I find where P lies - on $AB$ line sector or the continuation of $AB$. That's exactly what I don't understand - how to visualize the problem.
How do I figure out where exactly $P$ lies?
geometry vectors
edited Dec 10 '18 at 6:56
Ali
1,9732520
asked Dec 8 '18 at 9:02
Windy Windy
31
$endgroup$
"The position vectors of points $A$ and $B$ relative to the origin are
$3i+2j-k$ and $5i+6j+5k$ respectively. Find the position vector of the
point $P$ which lies on $AB$ produced such that $AP=3BP$."
Actually I can solve this, provided I find where P lies - on $AB$ line sector or the continuation of $AB$. That's exactly what I don't understand - how to visualize the problem.
How do I figure out where exactly $P$ lies?
geometry vectors
geometry vectors
edited Dec 10 '18 at 6:56
Ali
1,9732520
asked Dec 8 '18 at 9:02
Windy Windy
31
edited Dec 10 '18 at 6:56
Ali
1,9732520
asked Dec 8 '18 at 9:02
Windy Windy
31
edited Dec 10 '18 at 6:56
Ali
1,9732520
edited Dec 10 '18 at 6:56
Ali
1,9732520
edited Dec 10 '18 at 6:56
Ali
1,9732520
1,9732520
asked Dec 8 '18 at 9:02
Windy Windy
31
asked Dec 8 '18 at 9:02
Windy Windy
31
asked Dec 8 '18 at 9:02
Windy Windy
31
31
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Since it is written that "point P which lies on AB produced", therefore P doesn't lie on line AB and given is the case of external division.
Apply the external section formula directly.
Hope it is helpful.
answered Dec 8 '18 at 9:21
MartundMartund
1,633213
$endgroup$
$begingroup$
Thank you very much. That was it, I didn't understand the expression properly.
$endgroup$
– Windy
Dec 8 '18 at 9:24
add a comment |
$begingroup$
Here's my understanding of the problem:
The point $P$ is at $A + 3/4 (B-A)$.
answered Dec 8 '18 at 9:29
David G. StorkDavid G. Stork
11k41432
$endgroup$
$begingroup$
P lies on AB produced and not on AB as you are assuming.
$endgroup$
– Martund
Dec 8 '18 at 9:35
$begingroup$
What does "AB produced" mean?
$endgroup$
– David G. Stork
Dec 8 '18 at 11:40
$begingroup$
Means that you have to extend AB to get P on that, it is not on line segment AB.
$endgroup$
– Martund
Dec 8 '18 at 11:46
$begingroup$
"AB produced" is not standard English.
$endgroup$
– David G. Stork
Dec 8 '18 at 11:48
add a comment |
Your Answer
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Since it is written that "point P which lies on AB produced", therefore P doesn't lie on line AB and given is the case of external division.
Apply the external section formula directly.
Hope it is helpful.
answered Dec 8 '18 at 9:21
MartundMartund
1,633213
$endgroup$
$begingroup$
Thank you very much. That was it, I didn't understand the expression properly.
$endgroup$
– Windy
Dec 8 '18 at 9:24
add a comment |
$begingroup$
Since it is written that "point P which lies on AB produced", therefore P doesn't lie on line AB and given is the case of external division.
Apply the external section formula directly.
Hope it is helpful.
answered Dec 8 '18 at 9:21
MartundMartund
1,633213
$endgroup$
$begingroup$
Thank you very much. That was it, I didn't understand the expression properly.
$endgroup$
– Windy
Dec 8 '18 at 9:24
add a comment |
$begingroup$
Since it is written that "point P which lies on AB produced", therefore P doesn't lie on line AB and given is the case of external division.
Apply the external section formula directly.
Hope it is helpful.
answered Dec 8 '18 at 9:21
MartundMartund
1,633213
$endgroup$
Since it is written that "point P which lies on AB produced", therefore P doesn't lie on line AB and given is the case of external division.
Apply the external section formula directly.
Hope it is helpful.
answered Dec 8 '18 at 9:21
MartundMartund
1,633213
answered Dec 8 '18 at 9:21
MartundMartund
1,633213
answered Dec 8 '18 at 9:21
MartundMartund
1,633213
answered Dec 8 '18 at 9:21
MartundMartund
1,633213
1,633213
$begingroup$
Thank you very much. That was it, I didn't understand the expression properly.
$endgroup$
– Windy
Dec 8 '18 at 9:24
add a comment |
$begingroup$
Thank you very much. That was it, I didn't understand the expression properly.
$endgroup$
– Windy
Dec 8 '18 at 9:24
$begingroup$
Thank you very much. That was it, I didn't understand the expression properly.
$endgroup$
– Windy
Dec 8 '18 at 9:24
$begingroup$
Thank you very much. That was it, I didn't understand the expression properly.
$endgroup$
– Windy
Dec 8 '18 at 9:24
add a comment |
$begingroup$
Here's my understanding of the problem:
The point $P$ is at $A + 3/4 (B-A)$.
answered Dec 8 '18 at 9:29
David G. StorkDavid G. Stork
11k41432
$endgroup$
$begingroup$
P lies on AB produced and not on AB as you are assuming.
$endgroup$
– Martund
Dec 8 '18 at 9:35
$begingroup$
What does "AB produced" mean?
$endgroup$
– David G. Stork
Dec 8 '18 at 11:40
$begingroup$
Means that you have to extend AB to get P on that, it is not on line segment AB.
$endgroup$
– Martund
Dec 8 '18 at 11:46
$begingroup$
"AB produced" is not standard English.
$endgroup$
– David G. Stork
Dec 8 '18 at 11:48
add a comment |
$begingroup$
Here's my understanding of the problem:
The point $P$ is at $A + 3/4 (B-A)$.
answered Dec 8 '18 at 9:29
David G. StorkDavid G. Stork
11k41432
$endgroup$
$begingroup$
P lies on AB produced and not on AB as you are assuming.
$endgroup$
– Martund
Dec 8 '18 at 9:35
$begingroup$
What does "AB produced" mean?
$endgroup$
– David G. Stork
Dec 8 '18 at 11:40
$begingroup$
Means that you have to extend AB to get P on that, it is not on line segment AB.
$endgroup$
– Martund
Dec 8 '18 at 11:46
$begingroup$
"AB produced" is not standard English.
$endgroup$
– David G. Stork
Dec 8 '18 at 11:48
add a comment |
$begingroup$
Here's my understanding of the problem:
The point $P$ is at $A + 3/4 (B-A)$.
answered Dec 8 '18 at 9:29
David G. StorkDavid G. Stork
11k41432
$endgroup$
Here's my understanding of the problem:
The point $P$ is at $A + 3/4 (B-A)$.
answered Dec 8 '18 at 9:29
David G. StorkDavid G. Stork
11k41432
answered Dec 8 '18 at 9:29
David G. StorkDavid G. Stork
11k41432
answered Dec 8 '18 at 9:29
David G. StorkDavid G. Stork
11k41432
answered Dec 8 '18 at 9:29
David G. StorkDavid G. Stork
11k41432
11k41432
$begingroup$
P lies on AB produced and not on AB as you are assuming.
$endgroup$
– Martund
Dec 8 '18 at 9:35
$begingroup$
What does "AB produced" mean?
$endgroup$
– David G. Stork
Dec 8 '18 at 11:40
$begingroup$
Means that you have to extend AB to get P on that, it is not on line segment AB.
$endgroup$
– Martund
Dec 8 '18 at 11:46
$begingroup$
"AB produced" is not standard English.
$endgroup$
– David G. Stork
Dec 8 '18 at 11:48
add a comment |
$begingroup$
P lies on AB produced and not on AB as you are assuming.
$endgroup$
– Martund
Dec 8 '18 at 9:35
$begingroup$
What does "AB produced" mean?
$endgroup$
– David G. Stork
Dec 8 '18 at 11:40
$begingroup$
Means that you have to extend AB to get P on that, it is not on line segment AB.
$endgroup$
– Martund
Dec 8 '18 at 11:46
$begingroup$
"AB produced" is not standard English.
$endgroup$
– David G. Stork
Dec 8 '18 at 11:48
$begingroup$
P lies on AB produced and not on AB as you are assuming.
$endgroup$
– Martund
Dec 8 '18 at 9:35
$begingroup$
P lies on AB produced and not on AB as you are assuming.
$endgroup$
– Martund
Dec 8 '18 at 9:35
$begingroup$
What does "AB produced" mean?
$endgroup$
– David G. Stork
Dec 8 '18 at 11:40
$begingroup$
What does "AB produced" mean?
$endgroup$
– David G. Stork
Dec 8 '18 at 11:40
$begingroup$
Means that you have to extend AB to get P on that, it is not on line segment AB.
$endgroup$
– Martund
Dec 8 '18 at 11:46
$begingroup$
Means that you have to extend AB to get P on that, it is not on line segment AB.
$endgroup$
– Martund
Dec 8 '18 at 11:46
$begingroup$
"AB produced" is not standard English.
$endgroup$
– David G. Stork
Dec 8 '18 at 11:48
$begingroup$
"AB produced" is not standard English.
$endgroup$
– David G. Stork
Dec 8 '18 at 11:48
add a comment |
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