Question

THREE QUESTIONS HELP GIVING MEDALS
1.) Let u = <5, 6>, v = <-2, -6>. Find -2u + 5v.
<-20, -42>
<-20, 0>
<0, 18>
<-6, 0>
2.) Find the dot product, a · b.

a = 6i + 5j, b = -5i + 4j

50
<1, 9>
-10
<-30, 20>
3.) Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <7, 2>, v = <21, 6>

Neither
Orthogonal
Parallel
None of these

Answer 1

@DanJS

Answer 2

@Loser66

Answer 3

yeah

Answer 4

You can add similar dimensions for vectors, and you can multiply a vector by a constant scalar....

Answer 5

@SolomonZelman

Answer 6

c*<x,y> = <cx, cy>

Answer 7

<a,b> + <c,d> = <a+c , b+d>

Answer 8

those are the two rules for part 1

Answer 9

i literally hv no clue how to get an answer

Answer 10

ok.. , here is the first step, replacing u and v with the vectors given

-2u + 5v = -2*<5, 6> + 5*<-2, -6>

Answer 11

Now you can, by the first rule i gave, distribute the numbers into the vectors...

Answer 12

is it A?

Answer 13

havent looked at answers , not sure

Answer 14

-2u + 5v = -2*<5, 6> + 5*<-2, -6> = <-10, -12> + < -10, -30>

Answer 15

now use rule 2 that i gave

Answer 16

<-10, -12> + < -10, -30> = <-10+(-10) , -12 + (-30) >

Answer 17

@em2000 It is not hard, please learn how to solve it rather than rely on others. Follow @DanJS and you can do whatever you like.
Please, don't just guess the answer. YOu CAN do it by yourself.:)

Answer 18

thank u @DanJS

Answer 19

for #2 i got 50 and #3 i got neither, did u get those?

Answer 20

2-dimensional dot product for part 2

a = <6 , 5>
b = <-5 , 4>

a * b = 6*-5 + 5*4

Dot product, just add the product of each dimension

Answer 21

-10?

Answer 22

right

Answer 23

awesome, is 3 wrong?

Answer 24

For part 3, the notes to remember are,

if for 2 vectors A and B

A * B = 0 They are Orthogonal

One is a scalar multiple of the other, they are parallel, B = k*A or A = k*B

Answer 25

so they def not orthogonal

Answer 26

hint, the dot product is not zero, and try multiplying the first vector by 3

Answer 27

ohhh theyre parallel!!

Answer 28

yep

Answer 29

thank u so much you are great!!!

Answer 30

no prob, numbers are meaningless, just remember the 3 or 4 rules... good luck