Analytical mechanics/vectorshelp

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The discussion focuses on two questions regarding the vectors A and B, where A = ci + cj + 3k and B = ci + j - 2k. For part a, the user attempts to find a value of 'c' that makes vector A parallel to vector B, concluding that no such value exists since the cross product does not equal zero for the values calculated. In part b, the user equates the magnitudes of A and B to find 'c', resulting in an imaginary value of ±2i, leading to the conclusion that no real value of 'c' makes the lengths equal. Another participant suggests using the dot product for part a and confirms the imaginary result for part b. The discussion highlights the complexities of vector relationships in analytical mechanics.
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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!.
 
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fahd said:
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.
 

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