Question

Find a ⋅ b.

a = 9i + 5j, b = 4i + 3j

Answer 1

@amistre64

Answer 2

stack them vertically and multiply them down

Answer 3

a = 9i + 5j
b = 4i + 3j
------------
36i + 15j

Answer 4

<36,15>

Answer 5

correct, which can also be written in many different ways

Answer 6

Find a ⋅ b.

a = <5, 2>, b = <4, 5>

would this be <20,10>

Answer 7

no, 20+10

Answer 8

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

u = <8, 7>, v = <9, 7>

Answer 9

what about this?

Answer 10

youll need the dot product, and the lengths of each vector

Answer 11

20+10?

Answer 12

yes, dot product produces a scalar, not a new vector ....

Answer 13

so 30?

Answer 14

ignore the i j parts

a = 9i + 5j
b = 4i + 3j
------------
a.b 36 + 15 = ?

Answer 15

51

Answer 16

thats better :)

Answer 17

okay! so what about Find the angle between the given vectors to the nearest tenth of a degree.

u = <8, 7>, v = <9, 7>

Answer 18

u = <8, 7> ; length?
v = <9, 7> ; length?
-----------
dot

we will need to know these values

Answer 19

oh, and just as a cursory glance, they are both on the y=7 axis

Answer 20

-8.3°

1.7°

3.3°

13.3°

Answer 21

those are the possible answers

Answer 22

the options are immaterial at the moment

u = <8, 7> ; length?
v = <9, 7> ; length?
-----------
dot

im not going to do it for you :)

Answer 23

i dont even know where to begin

Answer 24

do i have to multiply agin?

Answer 25

i showed you how to do that dot, and you should know by this stage how to find the length of a vector

Answer 26

length is: square, add, sqrt

Answer 27

so i square the 8 add 7 and then find the sqrt. of that number?

Answer 28

u = <8, 7> ; sqrt(8^2+7^2)
v = <9, 7> ; sqrt(9^2+7^2)

Answer 29

oh okay

Answer 30

square the parts, add them together, and sqrt the results gives you length

Answer 31

the first is 10.63

Answer 32

now, the angle between them is defined by a formula\[cos(\alpha)=\frac{dot}{length_1*length_2}\]

Answer 33

second is 11.40

Answer 34

and the dot is the numbers multiplied right?

Answer 35

yes, multiply down, and add them up

Answer 36

121/10.63(11.40)

Answer 37

lol, add em across might be more visually adept

Answer 38

is that right?

Answer 39

72
49
121 good

and the lengths are most likely fine as well

Answer 40

take the arccos, or inverse cosine of that value to determine the angle

Answer 41

121/121.182

Answer 42

ok

Answer 43

i got .063

Answer 44

that does not seem right

Answer 45

i get 0.05778 radians

Answer 46

or about 3.3 degrees

Answer 47

oh okay

Answer 48

do you have time for two more?

Answer 49

when you approximate the sqrts, you introduce a small error

Answer 50

ohh okay!

Answer 51

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

u = <6, -2>, v = <2, 6>

Answer 52

dot = 0 defined perp

Answer 53

do i begin the same way? with the multiplication

Answer 54

of course, dotting is the same process ....

Answer 55

okay and if it is 0?

Answer 56

does that mean it would be neither?

Answer 57

umm, dot = 0 is perp. orthogonal is another term for perpendicular

Answer 58

oh okay. I did not know that!!!

Answer 59

Evaluate the expression:

v ⋅ w

Given the vectors:

r = <8, 8, -6>; v = <3, -8, -3>; w = <-4, -2, -6>

Answer 60

v.w is still a dot of v and w

Answer 61

so what is the r?

Answer 62

extra stuff that isnt used.

Answer 63

okay

Answer 64

so the answer would be 22?

Answer 65

if i order a burger and fries from McDonalds, the rest of the stuff on the menu is inconsequential

Answer 66

@amistre64

Answer 67

v = <3, -8, -3>
w = <-4, -2, -6>
------------------
-12+16+18 = ?

Answer 68

so is 22 right?

Answer 69

yes

Answer 70

thank you so much for all of your time! i really really really appreciate it!