Question

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

u = <10, 6>, v = <9, 5>

Orthogonal

Parallel

Neither

Answer 1

@Zekarias

Answer 2

Can u find the dot product of the two vectors?

Answer 3

u*v = 0 -> orthogonal
u*v = |u| * |v| ->parallel

Answer 4

6 and 9?

Answer 5

What are 6 and 9?

Answer 6

im confused. im not sure how to solve this, or find dot product.

Answer 7

given u = (u1,u2)
and v = (v1,v2)
the dot product is given by :
u*v = u1v1 + u2v2

Answer 8

\[u.v =|u||v|\cos(\theta)\]Then find \theta\

Answer 9

in our case : u*v = 10*9 + 6*5 = 90 + 30 = 120

now its not 0 then they are not orthogonal
we have to check now if 120 = |u||v|

|u| = sqrt(10^2 + 6^2) = sqrt(136)
|v| = sqrt(9^2 + 5^2) = sqrt(106)
120 = 120.066 ?
no .. so they are not parallel..

Answer 10

so its neither!

Answer 11

right

Answer 12

thank you mind helping me with one more problem?

Answer 13

ask

Answer 14

Find the angle between the given vectors to the nearest tenth of a degree.

u = <6, -1>, v = <7, -4>

20.3°

10.2°

0.2°

30.3°

Answer 15

so
u*v = |u|*|v|*cos(a)

we can calculate u*v using the coordinates : 6*7 + (-1)*(-4) = 46
now |u| = sqrt(6^2 + (-1)^2) = sqrt(37)
|v| = sqrt(7^2 + (-4)^2) = sqrt(49 + 16) = sqrt(65)

so we have :
46 = sqrt(37) * sqrt(65) * cos(a)
cos(a) = 46 / (sqrt(37) * sqrt(65))
a = arccos( 46 / (sqrt(37) * sqrt(65)))
a=20.28 is aprox a=20.3

Answer 16

thank you. you have been very helpful!

Answer 17

yw.. ill sleep now lol
have a good day

Answer 18

Express the complex number in trigonometric form.

-6i

6(cos 0° + i sin 0°)

6(cos 270° + i sin 270°)

6(cos 180° + i sin 180°)

6(cos 90° + i sin 90°)