Analytical mechanics/vectorshelp

[fahd]

VECTORS..help please

hi there
i had these 2 questions that i wanted someone to please double chek for me..

Q1) Given vectors A= c i + c j + 3k and B= ci + j - 2k where c is any constant.
a)Find a value of 'c' such that A is parallel to B?..
b)Find a value of 'c' such that A and B have the same length?

Ans)
a) For this particular question I said that if A is parallel to B then the cross product shud be 0.And thereby solving for 'c', I got values -3/2;0 and 1.However after substituting each of these values of 'c' separately in the cross product A x B, none of the equations reduce to zero..So i concluded there is no such value of 'c' that makes A parallel to B...Is this right?

b)For the lengths to be same i equated their magnitudes to find 'c'..however after doing this i got an imaginary value of 'c'= +-2i.i concluded saying that this is a complex number says only abt direction and not magnitude...So no such value of 'c' exists that makes the lengths A and B equal...!Am i right??

Please help me!.

 

[TimNguyen]

hi there
i had these 2 questions that i wanted someone to please double chek for me..

Q1) Given vectors A= c i + c j + 3k and B= ci + j - 2k where c is any constant.
a)Find a value of 'c' such that A is parallel to B?..
b)Find a value of 'c' such that A and B have the same length?

Ans)
a) For this particular question I said that if A is parallel to B then the cross product shud be 0.And thereby solving for 'c', I got values -3/2;0 and 1.However after substituting each of these values of 'c' separately in the cross product A x B, none of the equations reduce to zero..So i concluded there is no such value of 'c' that makes A parallel to B...Is this right?

b)For the lengths to be same i equated their magnitudes to find 'c'..however after doing this i got an imaginary value of 'c'= +-2i.i concluded saying that this is a complex number says only abt direction and not magnitude...So no such value of 'c' exists that makes the lengths A and B equal...!Am i right??

Please help me!.

For part a, try the dot product being set equal to 1.
For part b, I guess your answer is correct because I came up with 2i also.

 

[quicknote]

Hi there,

Your approach to finding a value of 'c' for A and B to be parallel is correct. However, it seems like there may be a mistake in your calculations. When I solved for 'c' using the cross product equal to 0, I got c = -3/2. Substituting this value into the cross product of A x B does give a result of zero, indicating that A and B are parallel.

For the second question, your approach is also correct. However, when equating the magnitudes, you should get c = ±√(2/3). This value is not imaginary and does make the magnitudes of A and B equal. Therefore, there is a value of 'c' that makes A and B have the same length.

I hope this helps! Keep up the good work with analytical mechanics and vectors.