# Vector problem! !

fahd

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..I concluded therefore no such value of 'c' exists..Was that 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??

Last edited:

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..However taking the dot product of the two vectors reveals a different answer altogether..(i think 'c'=2)...WHAT DO I CONCLUDE?

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??

part a: ...don't deal with cross-products. there's a MUCH easier way!

use the fact that if two vectors are parallel to each other, than they must be some constant multiple of each other.

you can find this multiple by dividing the k-hat coefficient for one of the vectors by the k-hat coefficient for the other one. then simply use that ratio to figure out the other terms.

...wait a minute. looking at the i-hat coefficients, you'll be dividing c by c. this is 1 (independent of the choice of c), clearly, so... there is no solution, since the ratio of the k-hat coefficients are not 1.

that's lame!

part b: the magnitude of a vector is given by the 3-d version of the pythagorean theorem. apply that to each vector and set'em equal to each other and solve the resulting algebraic equation.

...ah, crap. i got an answer of c = 2i or c = -2i, as well. :yuck:

we're dealing with the vector space R^3, which is a vector space over the field the real numbers. so we can't have complex numbers in there.

so i guess you should just say "no real number c exists such that the vectors have the same magnitude," after showing that you get imaginary solutions.

fahd