some conceptual understanding of vectors...

[Phantom-II]

Hi. I just did the mav2012 and theres a few things i dont quite understand:
1. how can you have a negative scalar resolute? If i view from the 3D vector's flat plane and it is leaning to the right, does that mean i am taking a resolute that points to the left, which then will need a component that is greater than the original vector?

2. With angles between vectors/axis, should it always be positive ( i know its tail-to-tail, but cos(x)=cos(-x) etc ), or the smaller angle of the complementary pair? ( ie sqrt3i+1j, would the angle be 30 degrees or 150 degrees, or both accepted?)

[Jenny_2108]

Hi. I just did the mav2012 and theres a few things i dont quite understand:
1. how can you have a negative scalar resolute? If i view from the 3D vector's flat plane and it is leaning to the right, does that mean i am taking a resolute that points to the left, which then will need a component that is greater than the original vector?

2. With angles between vectors/axis, should it always be positive ( i know its tail-to-tail, but cos(x)=cos(-x) etc ), or the smaller angle of the complementary pair? ( ie sqrt3i+1j, would the angle be 30 degrees or 150 degrees, or both accepted?)

1. Scalar just means no direction so it can positive or negative
2. Nope, depends on the vectors. It can be >180 degress. You know its tail-to-tail so from the graph, you will decide 30 or 150 degrees

I'm a bit crazy atm so if I answer wrong, someone correct me

[BubbleWrapMan]

The angle between two vectors is taken as the smallest angle between them when they are tail-to-tail, and this is always in .

You get a negative scalar resolute when said angle is in .

[Phantom-II]

ah i see, i think i understand now. thank you guys!

im going thru the vcaa 07, and the solution for question 8c slope field has only one curve sketched. I think there should be an asymptote within the domain since its a tan graph, at -pi/2 which is ~-1.6, as well as another curve from around ~(-3, 1) . Should there only be one curve in a slopefield?

[BubbleWrapMan]

Yes, usually the solution to a differential equation needs to be continuous