Question

Determine if the vectors are orthogonal, parallel or neither v = <3i - 5j>, w=< -9i +10j

Answer 1

What's the dot product of the two vectors?

Answer 2

That's all I have

Answer 3

well.. do you know how to find the dot product of two vectors? I assume this has already been covered

depending on the dot product of the two vectors, you can see if they're such
if 0 is the dot product, then they are orthogonal

and they're parallel if their coordinates are multiplies of each other

Answer 4

when I did the problem and the answer I got wasn't zero nor was it a multiple of each other. so I assumed it was neither

Answer 5

yeap, then is neither

Answer 6

is that the same answer you got?

Answer 7

A non-zero dot product only guarantees that the two vectors aren't orthogonal. To check if they're parallel or neither, you have to use a handy formula:
\[a\cdot b=|a||b|\cos\theta\]
where \(a\) and \(b\) are the given vectors, \(|a|\) and \(|b|\) are their respective magnitudes, and \(\theta\) is the angle between them.

Answer 8

If the angle is 0 or 180 degrees, they're parallel. Otherwise, neither.

Answer 9

\(\bf \textit{angle between two vectors }\\ \quad \\
cos(\theta)=\cfrac{u \cdot v}{||u||\ ||v||} \implies \cfrac{\text{dot product}}{\text{product of magnitudes}}\\ \quad \\
\theta = cos^{-1}\left(\cfrac{u \cdot v}{||u||\ ||v||}\right)\)

Answer 10

on the other hand, they're not multiple of each other =)

Answer 11

thanks Guys

Answer 12

yw