Question

Determine a and b so that the vectors < 1,3a+b,2 > and < 2,−1,a+ b > are parallel.

Answer 1

would i set up 3a+b=-1

Answer 2

if they're parallel one should be a scalar multiple of the other.
as such the second should be double the first.
set up the equations in that way

Answer 3

3a+b=-(1/2)
a+b = 4

Answer 4

where did you get the <-1/2> from

Answer 5

the econd vector should be double the first

Answer 6

i was thinking more along the lines of <1,3a+b,2>=S<2,-1,a+b>

Answer 7

let u = <1, 3a+b, 2> and 2u = <2, 6a+2b, 4>, right?
v= <2, -1, a+b> and if v = 2u then
6a+2b=-1 => 3a+b = -(1/2)
a+b = 4

Answer 8

ok i understand that but arent they looking for a +b individually or it doesnt matter

Answer 9

yes and you have a system of 2 equations in 2 unknowns... solve using whatever method you prefer.

Answer 10

okay thx

Answer 11

you're welcome... does it all make sense now?

Answer 12

yea

Answer 13

cool!