Find a non-zero vector u with terminal point Q(3,0,-5) such that u is opp directed to v=(4,-2,-1)?
$begingroup$
So for this question, this is how i approach
Let's treat initial point as (a1,a2,a3) and we got the terminal point, so vector of u is (3-a) (0-b) and (-5-c)
I am kind of stuck here as I as if the question was same direction, we just need to find the scalar multiple but opposite direction, how do we approach?
Thanks for the help in advance :)
vectors
asked Aug 30 '15 at 15:55
OngOng
318
$endgroup$
add a comment |
$begingroup$
So for this question, this is how i approach
Let's treat initial point as (a1,a2,a3) and we got the terminal point, so vector of u is (3-a) (0-b) and (-5-c)
I am kind of stuck here as I as if the question was same direction, we just need to find the scalar multiple but opposite direction, how do we approach?
Thanks for the help in advance :)
vectors
asked Aug 30 '15 at 15:55
OngOng
318
$endgroup$
add a comment |
$begingroup$
So for this question, this is how i approach
Let's treat initial point as (a1,a2,a3) and we got the terminal point, so vector of u is (3-a) (0-b) and (-5-c)
I am kind of stuck here as I as if the question was same direction, we just need to find the scalar multiple but opposite direction, how do we approach?
Thanks for the help in advance :)
vectors
asked Aug 30 '15 at 15:55
OngOng
318
$endgroup$
So for this question, this is how i approach
Let's treat initial point as (a1,a2,a3) and we got the terminal point, so vector of u is (3-a) (0-b) and (-5-c)
I am kind of stuck here as I as if the question was same direction, we just need to find the scalar multiple but opposite direction, how do we approach?
Thanks for the help in advance :)
vectors
vectors
asked Aug 30 '15 at 15:55
OngOng
318
asked Aug 30 '15 at 15:55
OngOng
318
asked Aug 30 '15 at 15:55
OngOng
318
asked Aug 30 '15 at 15:55
OngOng
318
asked Aug 30 '15 at 15:55
OngOng
318
318
add a comment |
add a comment |
1 Answer
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$begingroup$
I'm going to assume that they mean that the vector we're looking for has to have the same magnitude as the one from the origin to <4,-2,-1> even though the problem doesn't specify that. Otherwise, there are many possible solutions to this problem.
So, the vector we are looking for is in the direction
$vec u$ =<-4,2,1>, which is the opposite direction of the vector <4,-2,-1>. That's our slope. And the magnitude must equal $sqrt 21$
Starting from the original point (a,b,c) and terminating at (3,0,-5),
we're looking for where
3 - a = -4
0 - b = 2 and
-5 - c = 1
solving these equations, we come up with an original point (7,-2,-6).
Here's a graph that shows that these two vectors have the same magnitude and opposite direction: http://www.bodurov.com/VectorVisualizer/?vectors=0/0/0/4/-2/-1v7/-2/-6/3/0/-5
answered Aug 30 '15 at 19:28
JHSJHS
459216
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add a comment |
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1 Answer
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1 Answer
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$begingroup$
I'm going to assume that they mean that the vector we're looking for has to have the same magnitude as the one from the origin to <4,-2,-1> even though the problem doesn't specify that. Otherwise, there are many possible solutions to this problem.
So, the vector we are looking for is in the direction
$vec u$ =<-4,2,1>, which is the opposite direction of the vector <4,-2,-1>. That's our slope. And the magnitude must equal $sqrt 21$
Starting from the original point (a,b,c) and terminating at (3,0,-5),
we're looking for where
3 - a = -4
0 - b = 2 and
-5 - c = 1
solving these equations, we come up with an original point (7,-2,-6).
Here's a graph that shows that these two vectors have the same magnitude and opposite direction: http://www.bodurov.com/VectorVisualizer/?vectors=0/0/0/4/-2/-1v7/-2/-6/3/0/-5
answered Aug 30 '15 at 19:28
JHSJHS
459216
$endgroup$
add a comment |
$begingroup$
I'm going to assume that they mean that the vector we're looking for has to have the same magnitude as the one from the origin to <4,-2,-1> even though the problem doesn't specify that. Otherwise, there are many possible solutions to this problem.
So, the vector we are looking for is in the direction
$vec u$ =<-4,2,1>, which is the opposite direction of the vector <4,-2,-1>. That's our slope. And the magnitude must equal $sqrt 21$
Starting from the original point (a,b,c) and terminating at (3,0,-5),
we're looking for where
3 - a = -4
0 - b = 2 and
-5 - c = 1
solving these equations, we come up with an original point (7,-2,-6).
Here's a graph that shows that these two vectors have the same magnitude and opposite direction: http://www.bodurov.com/VectorVisualizer/?vectors=0/0/0/4/-2/-1v7/-2/-6/3/0/-5
answered Aug 30 '15 at 19:28
JHSJHS
459216
$endgroup$
add a comment |
$begingroup$
I'm going to assume that they mean that the vector we're looking for has to have the same magnitude as the one from the origin to <4,-2,-1> even though the problem doesn't specify that. Otherwise, there are many possible solutions to this problem.
So, the vector we are looking for is in the direction
$vec u$ =<-4,2,1>, which is the opposite direction of the vector <4,-2,-1>. That's our slope. And the magnitude must equal $sqrt 21$
Starting from the original point (a,b,c) and terminating at (3,0,-5),
we're looking for where
3 - a = -4
0 - b = 2 and
-5 - c = 1
solving these equations, we come up with an original point (7,-2,-6).
Here's a graph that shows that these two vectors have the same magnitude and opposite direction: http://www.bodurov.com/VectorVisualizer/?vectors=0/0/0/4/-2/-1v7/-2/-6/3/0/-5
answered Aug 30 '15 at 19:28
JHSJHS
459216
$endgroup$
I'm going to assume that they mean that the vector we're looking for has to have the same magnitude as the one from the origin to <4,-2,-1> even though the problem doesn't specify that. Otherwise, there are many possible solutions to this problem.
So, the vector we are looking for is in the direction
$vec u$ =<-4,2,1>, which is the opposite direction of the vector <4,-2,-1>. That's our slope. And the magnitude must equal $sqrt 21$
Starting from the original point (a,b,c) and terminating at (3,0,-5),
we're looking for where
3 - a = -4
0 - b = 2 and
-5 - c = 1
solving these equations, we come up with an original point (7,-2,-6).
Here's a graph that shows that these two vectors have the same magnitude and opposite direction: http://www.bodurov.com/VectorVisualizer/?vectors=0/0/0/4/-2/-1v7/-2/-6/3/0/-5
answered Aug 30 '15 at 19:28
JHSJHS
459216
edited Aug 30 '15 at 19:45
answered Aug 30 '15 at 19:28
JHSJHS
459216
answered Aug 30 '15 at 19:28
JHSJHS
459216
answered Aug 30 '15 at 19:28
JHSJHS
459216
459216
add a comment |
add a comment |
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