Question

determine whether u and v are orthogonal, parallel, or neither

Answer 1

u = <-5/3,7/2> v=<10,-21>

Answer 2

its not neither and its not orthogonal SO IT IS PARALLEL BUT HOW DO i figure that out

Answer 3

If the dot product between two vectors is zero they are perpendicular to each other. If they are multiples of each other they are parallel.

If you want to solve for the angle between them use the defintion of the dot product which is,

\[U .V = \left| U \right|\left| V \right|\cos \theta \]

Just solve for theta.

Hope this helps :)

Answer 4

so i do the dot product and it is (-5/3)(10)+(7/2)(-21)=-541/6

Answer 5

so that means they are not orthogonal.
to find that they are parallel or neither u would find the angle in between? @Schrodingers_Cat

Answer 6

Yes, they are not orthogonal and if they are not multiples of each other then are not parallel. So, check and see if they are multiples of each other :)

Answer 7

how do u do that? we didn't learn that?

Answer 8

Take the ratio of each components namely

10/(-5/3) = -6

-21/(7/2) = -6

Since its the same ratio they are multiples of -6 and are parallel.

:)

Answer 9

okay can u help with another?

Answer 10

Sure :)

Answer 11

given vectors u=<4,5> and v=<-5,-3> determine the quality indicated by (3u.2v)u

Answer 12

So, you want (3U dot 2V)U correct?

Answer 13

yes

Answer 14

If so multiply vector U by 3 then vector V by 2. After that take the dot product between them and you will have a scalar value of which you just multiply U by.

It will look like this

\[((3(4)), (3(5)) . (2(-5),(2(-3))<4,5>\]

Answer 15

which i did. the u on the outside would be the magnitude of u right?

Answer 16

No, just the vector u.

Answer 17

(12(-10) + 15(-6)) <4,5>?

Answer 18

Yep looks right :)

Answer 19

so then it would be (-210)<4,5>

Answer 20

would that be your answer?

Answer 21

Hope this helps :)

Answer 22

that would be your answer though? @Schrodingers_Cat