## anonymous 5 years ago For what values of t, if any, is given vector parallel to vector u = (4,-1): (8t, 2t)? and (1,t^2)?

1. amistre64

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

2. amistre64

4 = 8t -1 = 2t

3. amistre64

it can also be in the opposit direction and be parallel

4. amistre64

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

5. anonymous

what is it possible?

6. anonymous

are you talking about the first one or second?

7. anonymous

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

8. amistre64

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

9. anonymous

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

10. 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

11. anonymous

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

12. anonymous

I just can't completely find t when I tried

13. amistre64

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

14. anonymous

ohh that's makes more sense thanks!

15. amistre64

youre welcome :)

16. anonymous

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

17. anonymous

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

18. 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

19. amistre64

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

20. amistre64

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

21. amistre64

they are orthoganal vector

22. amistre64

maybe not ortho; but no the same slope :)

23. anonymous

sry. what does <> mean?

24. amistre64

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

25. amistre64

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

26. anonymous

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

27. amistre64

correct

28. anonymous

for $t \in R$

29. amistre64

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

30. anonymous

thanks :)