Question

Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <6, 4>, v = <-9, 8>

Answer 1

use dot product
\[u*v = (6*-9)+(4*8) = -22\]
vectors are orthogonal only if dot product is zero

Answer 2

so its not orthogonal,, its parallel or neither then right?

Answer 3

vectors are only parallel if they are proportional ..... <1,2> and <3,6>

so answer is neither

Answer 4

ohh ! ok thank you, do u have time to help me with one more?

Answer 5

ok

Answer 6

Given that P = (-5, 5) and Q = (-13, 6), find the component form and magnitude of 2PQ

Answer 7

so far i think its, <-16, 2> now i just have to find the magnitude

Answer 8

hmm you can't do the cross-product of 2-d vectors and get a vector ?

Answer 9

huh?

Answer 10

what do they mean by PQ?

Answer 11

im not really sure thats why im comfused

Answer 12

im stuck on this problem and this one Find the fifth roots of 243(cos 240° + i sin 240°).

Answer 13

to find 5th root .... take 5th root of 243 and divide angle by 5

Answer 14

i have to find the five roots to that equation i think?

Answer 15

right
\[= 3(\cos (48+k \pi)+i \sin(48 +k \pi))\]
where k = 0,1,2,3,4

Answer 16

yeah, so what else would i do then from there?

Answer 17

sorry , pi should be 180 since you are in degrees
oh wait i am wrong...forgot something
\[= 3(\cos (\frac{240+180k}{5})+i \sin(\frac{240+180k}{5}))\]

Answer 18

so thats the answer? now im comfused? what would i show as steps?

Answer 19

plug in each value for k and those are the 5 roots

Answer 20

oh so plug the 0,1,2,3,4 into where the k is and thats it?

Answer 21

yeah

Answer 22

how should i plug in the isin in the calculator

Answer 23

i just get decimals when i plug them in?