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Mathematics 54 Online
OpenStudy (anonymous):

For what values of t, if any, is given vector parallel to vector u = (4,-1): (8t, 2t)? and (1,t^2)?

OpenStudy (amistre64):

the vector would have to be a scalar of (4,-1) in order to be parallel to it

OpenStudy (amistre64):

4 = 8t -1 = 2t

OpenStudy (amistre64):

it can also be in the opposit direction and be parallel

OpenStudy (amistre64):

-1/4 is the slope we want to obtain right?

OpenStudy (anonymous):

what is it possible?

OpenStudy (anonymous):

are you talking about the first one or second?

OpenStudy (anonymous):

b/c the second one I got -1/4 and I can't square root it

OpenStudy (amistre64):

the second one cant be parallel; there is no hope of a negative slope with it

OpenStudy (anonymous):

and the first one I can't get a value that's works because one of them needs to be negative?

OpenStudy (amistre64):

thats the way i see it as well; the cant hav the same direction as the original no matter what real values you plug in

OpenStudy (anonymous):

okay so the second one doesn't work I can't explain it

OpenStudy (anonymous):

I just can't completely find t when I tried

OpenStudy (amistre64):

t^2 is always positive; no way to get a negative slope

OpenStudy (anonymous):

ohh that's makes more sense thanks!

OpenStudy (amistre64):

youre welcome :)

OpenStudy (anonymous):

@amistre64: why has the vector be a scalar of (4,-1), it can be any scalar(4x,-1x) isn't it?

OpenStudy (anonymous):

allsmiles: is the question asking that both the vectors (8t,2t) and (1,t^2) should be parallel simultaneously or independently?

OpenStudy (anonymous):

The first one is always parallel, whatever the value of t be, the second one is parallel (or anti-parallel) when t = +- 1/2

OpenStudy (amistre64):

a scalar of (4,-1) simply means that any scalar will do

OpenStudy (amistre64):

t<8,2> != x<4,-1> no matter what you do to it right?

OpenStudy (amistre64):

they are orthoganal vector

OpenStudy (amistre64):

maybe not ortho; but no the same slope :)

OpenStudy (anonymous):

sry. what does <> mean?

OpenStudy (amistre64):

<> denotes a vector as opposed to () which is a point

OpenStudy (amistre64):

<3,5> is a vector; (3,5) is a point

OpenStudy (anonymous):

Oh, so for no value of t are any of the two vecs parallel, isnt it?

OpenStudy (amistre64):

correct

OpenStudy (anonymous):

for \[t \in R\]

OpenStudy (amistre64):

the question asked shows point notation; but is assumed to be vectors :)

OpenStudy (anonymous):

thanks :)

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