Determine whether the vectors u and v are parallel, orthogonal, or neither. u = , v =

Question

Determine whether the vectors u and v are parallel, orthogonal, or neither. u = <10, 0>, v = <0, -9>

anonymous · Answer

Do you know about the dot product?

anonymous · Answer

Yea Sorry i was in the restroom :o

anonymous · Answer

@wio

anonymous · Answer

Then what do you get when you do the dot product?

anonymous · Answer

0?

anonymous · Answer

Okay, so what does it mean if the dot product between two vectors is 0?

anonymous · Answer

Is it parallel?

anonymous · Answer

<0,1> and <0,1> are identical vectors... clearly they are parallel. The dot product is 1. Thus I don't think it means that.

anonymous · Answer

so neither since there is no dot product D:

anonymous · Answer

No, the remaining options are  orthogonal and neither.

anonymous · Answer

so its orthogonal if it isnt neither?

anonymous · Answer

Im sorry i just dont know how to find these :(

anonymous · Answer

It is either orthogonal or it is neither, but we need to find out first.

anonymous · Answer

Can you think of two vectors which are orthogonal?

Do you know what orthogonal means?

anonymous · Answer

perpendicular

anonymous · Answer

okay, so can you think of two perpendicular vectors?

anonymous · Answer

i dont know :/

anonymous · Answer

Perpendicular means the angle between to vectors is $90^\circ$.
The dot product is equal to $\|\mathbf v_1\|\|\mathbf v_2\|\cos\theta$

anonymous · Answer

okay

anonymous · Answer

Where $\theta$  is the angle between the vectors.
Is this familiar at all?

anonymous · Answer

Yea alittle

anonymous · Answer

So what is $\cos 90^\circ$?

anonymous · Answer

ohhhhh Cos90=0

anonymous · Answer

so when the dot product is 0 it is perpendicular

anonymous · Answer

This is something that is supposed to be obvious.

anonymous · Answer

Well i apologize then. Can you help me with one more?

anonymous · Answer

Let u = <-6, -2>, v = <-2, 3>. Find -3u + 2v.

anonymous · Answer

What is it?

anonymous · Answer

okay do you know how to multiply a vector by a scalar?

anonymous · Answer

i believe what i was told to do it -2(-6+-2) 2(-2,3) is that right?

anonymous · Answer

No, that is not correct.  The answer will be a vector, not a number.

anonymous · Answer

oh then no i don't know

anonymous · Answer

Can you explain how to do it? :o

anonymous · Answer

Okay, so first what is $-3\mathbf u$ equal to?

anonymous · Answer

Hint: it is another vector.

anonymous · Answer

$-3$ is a scalar and $\mathbf u$ is a vector... what happens when you multiply them?