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- anonymous

Determine whether the vectors u and v are parallel, orthogonal, or neither.
u = <7, -4>, v = <-28, 16>
Is the correct answer neither?

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- anonymous

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- phi

do you know how to do a "dot product" ?
multiply corresponding elements and then add
if you get 0, the vectors are perpendicular (orthogonal, and form a 90 angle)
you can also factor 4 from v to write it as 4<-7,4>
the 4 "out front" does not change the direction, so you need only work with <-7,4>

- anonymous

@phi I did not get zero. I thought that the answer was neither, is that correct?

- Jhannybean

Since you tested out the dot product and found that it does not equal 0, you know they are not perpendicular.
Now test if these two are parallel by taking the dot product of their magnitudes and comparing the dot product of their magnitudes to the dot product of the two vectors you found earlier.
If you end up with the same result, then you know the vectors are parallel :)

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- phi

yes, they are not perpendicular.
the other trick is to notice what we get if we factor -4 from v
v = <-28, 16>
v = -4<7,-4>
we can't factor anything else out, so it is in simplest from
but notice u = <7,-4>
u and v point in the same direction (but v is "longer")
in other words, they are parallel.

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