Resultant Vector

  • #1
Muhammad Danish
70
7
According to my understanding, option D is the only possible value of R. I don't understand how options A, B and C are included. Please explain this question.
Thanks.
(regards)
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Answers and Replies

  • #2
drvrm
963
214
According to my understanding, option D is the only possible value of R. I don't understand how options A, B and C are included. Please explain this question.
Thanks.
(regards)

just try to check the values of resultant at 0 and 90 degrees
anything outside this range of R is not possible.
 
  • #3
Muhammad Danish
70
7
just try to check the values of resultant at 0 and 90 degrees
anything outside this range of R is not possible.
I do not understand...
 
  • #4
drvrm
963
214
I do not understand...

in the question the angles are given between zero and ninety degree
so if you put zero
then the two vectors are collinear so they will add up that gives you a value of R
i think that is maximum value
similarly put them at 90 degree
 
  • #5
Muhammad Danish
70
7
in the question the angles are given between zero and ninety degree
so if you put zero
then the two vectors are collinear so they will add up that gives you a value of R
i think that is maximum value
similarly put them at 90 degree
If we put them at 90 degrees, then the vectors will still add up to 7 N, won't they?
 
  • #7
drvrm
963
214
If we put them at 90 degrees, then the vectors will still add up to 7 N, won't they?

two vectors at an angle theta then there is a rule parallelogram -law
R = sqrt{ 3^2 + 4^2 + 2 (3*4 ) cos (theta) }
so if theta =90
cos 90 =0
 
  • #8
Muhammad Danish
70
7
  • #10
Muhammad Danish
70
7
two vectors at an angle theta then there is a rule parallelogram -law
R = sqrt{ 3^2 + 4^2 + 2 (3*4 ) cos (theta) }
so if theta =90
cos 90 =0
Oh I understand now, it means that if we put Cos 90, then the answer will be the lowest value. Similarly if we put Cos 0, then the outcome will be the maximum value. Maximum value=7 Minimum Value=5 so 4N is not possible. Am I correct?
 
  • #11
Muhammad Danish
70
7
Then you know that, unless they are co-linear and pointing in the same direction, their resultant magnitude can't be 7.
When they will be co-linear, the resultant magnitude will be 7N, and when they are perpendicular to each other then the resultant magnitude will be 5N, so the value of R must lie between 5-7N. In the above MCQ the answer will be A.4N because it is not a possible value of R. Am I right?
 
  • #12
22,145
5,079
When they will be co-linear, the resultant magnitude will be 7N, and when they are perpendicular to each other then the resultant magnitude will be 5N, so the value of R must lie between 5-7N. In the above MCQ the answer will be A.4N because it is not a possible value of R. Am I right?
Yes.
 
  • #14
Muhammad Danish
70
7
two vectors at an angle theta then there is a rule parallelogram -law
R = sqrt{ 3^2 + 4^2 + 2 (3*4 ) cos (theta) }
so if theta =90
cos 90 =0
Thanks a lot! I understand now!!
 
  • #15
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
38,453
7,965
if we put Cos 90, then the answer will be the lowest value
Within the range specified, yes, but more generally the lowest value will be when the vectors oppose each other, i.e. θ=180°, cos(θ)=-1.
 

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