Question

Evaluate the expression. r = <9, -7, -8>, v = <3, 4, 7>, w = <6, -9, 7> v ⋅ w
PLEASE HELP ME! Ive been on forever and nobody has been able to help

Answer 1

you have formula to calculate dot product, just apply.
v.w = (3*6)+(4*(-9)+(7*7) = some number.
I saw this question once but I ignore because I think it's not a problem , you just apply formula, if you don't know that formula, look at mine, or look up at your note. i'm pretty sure that you have many questions similar those stuffs . try to figure out by yourself

Answer 2

So its 31?

Answer 3

@zepdrix why do you stop?

Answer 4

Yah 31 sounds right! :)

Oh I just thought it was strange that they gave you some vector \(\large \vec r\) and you don't even use it.
Was this information given for a series of questions I guess? :o
Or maybe the \(\large \vec r\) was just to confuse you :3

Answer 5

It was only one question . I was given the choices of ' <-27, 28, 56> <18, -36, 49>,
18 or 31 and when i calculated it i got 31. so thats correct?

Answer 6

Yes that's correct c:

Answer 7

ok thanks do you think you could help me with another?

Answer 8

@zepdrix ?

Answer 9

Sure.

Answer 10

The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used.

C = 37°, a = 19, c = 8

A = 90.6°, B = 52.4°, b ≈ 14

A = 52.4°, B = 90.6°, b ≈ 14

The triangle cannot be solved with the Law of Sines.

No triangle is formed

Answer 11

could you explain how i am supposed to do this because i get confused when trying to use the law of sines

Answer 12

@zepdrix ?

Answer 13

So is the part that's given to us `C = 37°, a = 19, c = 8`,

While the rest is multiple choice answers?

Answer 14

yes

Answer 15

Ok gimme a sec c:

Answer 16

So let's draw a triangle just for fun.

Answer 17

fancy

Answer 18

Let's try to use the Law of Sines and see what happens.

\(\huge \dfrac{\color{orangered}{a}}{sin A}=\dfrac{\color{orangered}{c}}{sin \color{orangered}{C}}\)

The Law of Sines tells us that we can relate the sides and angles in the given way.
The reason we're not involving the B's yet is because we were GIVEN these orange terms. Making it possible to solve for the 4th one in our equation.

Answer 19

so 19/sinA =8/sin37

Answer 20

Ok good, let's solve for sinA from here.

Answer 21

how?

Answer 22

Multiply both sides by sin A, giving us,
\[\large 19=\frac{8}{\sin 37}\sin A\]
Then we'll multiply both sides by sin 37,\[\large 19\sin 37=8\sin A\]Then finally, divide both sides by 8,\[\large \sin A=\frac{19\sin37}{8}\]

We had to jimmy some things around, but we were able to do it.

Answer 23

ohh okay!! so A is -1.5

Answer 24

Hold on -1.5 that mean that no triangle happens?

Answer 25

Hold on! Simmer down now! We still have some work to do! :)

Answer 26

oh ok . sorry

Answer 27

If you punch all that into your calculator, you should come up with,\[\large \sin A=1.43\]

But we ultmiately want to solve for \(\large A\), not \(\large \sin A\).
So we'll rewrite this using the Inverse Sine function.\[\large \sin A=1.43 \qquad \rightarrow \qquad A=\arcsin 1.43\]

Answer 28

Why did i get negative?

Answer 29

Hmm I dunno, are you sure you're in `degree mode` on your calculator?
It should be positive.

Answer 30

okay i redid it on my other calculator and got 1.42

Answer 31

im not sure why its not working on my graphing calculator

Answer 32

Yah you're in radians mode on your graphing calculator :) Just switch over to degrees.

Answer 33

it was in RADIANS!!! Thats why!! i hope it didnt screw up any of the other problems that ive been doing :/

Answer 34

UH OH! :O

Answer 35

ok so where do we go from here?

Answer 36

When we try to solve for A, using the Inverse Sine Function, we get an error on our calculator.

Which either meanssssss,
~It doesn't form a triangle, or,
~Maybe A is an obtuse angle.

Grr I can't remember how to do these darn Law of Sines problems :p it's been so long.

Answer 37

i think it doesn't form one

Answer 38

How would i do one of these problems when they say that two triangles are made from whatever they give you

Answer 39

Mmmmmmmmmmmmmmmmm I can't remember :C

Answer 40

What about turning complex numbers into trig form?

Answer 41

cause i can do it with no problem when i turn the trig form back into complex but i have a problem doing it the other way

Answer 42

Well thank you for your help anyways :) Have a good night