Are two vectors with opposite angles parallel to each other?

[devanlevin]

if two vectors, \vec{A} and \vec{B} have opposite angles, \vec{A}=(3,-2) \vec{B}=(-3,2) for example, are they considered parralel to each other even though they are in opposite directions

 

[HallsofIvy]

They are "anti-parallel". "Parallel" for vectors is not quite the same thing as parallel for lines in geometry. For example, we would certainly say that the vectors <2, 1> and <6, 3> are parllel but the lines given by (2t, t) and (6t, 3t) are NOT "parallel". In fact, they are different representations of the same line.

 

[devanlevin]

in the question i am asking about i am told that vector A is parallel to vector B, and i am supposed to give coordinates of B, am i meant to give just the coordinates of the vector in the same direction or both that and the opposing direction??

 

[HallsofIvy]

The question doesn't make sense. There are an infinite number of vectors parallel to a given vector A. What other conditions are you given for B?

 

[devanlevin]

thats not really relevant, just wanted to know if i must give both vectors or just the 1
anyway
Vector E is parallel to Vector F, E=5cm F=(6,-7)
what are the values of E

 

[Skatch]

If E is 5cm, then Sqrt[x^2+y^2] must equal 5cm. And if its parallel to F, it must have the same angle with respect to x-hat, that is ArcTan[y/x] must equal ArcTan[-7/6], which implies -7x = 6y. Two equations and two unknowns. You'll get two possible vectors, one parallel and one anti-parallel.

 

[devanlevin]

You'll get two possible vectors, one parallel and one anti-parallel.

so in my answer must i just give the parallel vector, not the anti parallel one?