Help with vectors please!
Consider two unit vectors u and v, where u x v = -1. Look at all the linear combinations of u and v;
{au + bv : a, b element of Real numbers}
Which geometrical object(s) (eg. point, plane, circle) does this set represent? Give a reasoned answer.

Question

Help with vectors please!
Consider two unit vectors u and v, where u x v = -1. Look at all the linear combinations of u and v;
{au + bv : a, b element of Real numbers}
Which geometrical object(s) (eg. point, plane, circle) does this set represent? Give a reasoned answer.

ganeshie8 · Answer

Are you really sure that is a x product ?

4meisu · Answer

Hi ganeshi, this is what the problem looks like:

ganeshie8 · Answer

It is a $\bullet$ product
Not $\times$ product

Those two symbols have different meanings in vector algebra

4meisu · Answer

Got it, thanks

ganeshie8 · Answer

Remember the formula for dot product ?

4meisu · Answer

Yes. I have found that x = pi, though I'm not sure what this means in terms of a geometrical object.

ganeshie8 · Answer

How do the vectors look like when the angle between them is 180 ?

4meisu · Answer

Not sure. A straight line?

ganeshie8 · Answer

Yes
Can u draw two vectors that have 180 degrees between them?

4meisu · Answer

Yes

ganeshie8 · Answer

Draw them here

4meisu · Answer

Wait that means that they are parallel

ganeshie8 · Answer

They are in opposite directions

ganeshie8 · Answer

Take one of them and multiply it by a number and think of the vector that u get

ganeshie8 · Answer

Multiplying a vector by a number only scales the vector. It doesn't change the direction

4meisu · Answer

So am I right in saying that the geometric shape is a straight line

ganeshie8 · Answer

Yep a straight  line

ganeshie8 · Answer

http://www.geogebra.org/m/F2RWHFyy?doneurl=%2Fganeshie8