Vector calculus problem: ||v||=17 where the i- component of v is 8i.

C

Christian.

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Good afternoon
I don't know where to start on this problem. Need some hints. Thanks.


Part A:
Find all vectors V in 2 dimensions having ||v||=17 where the i- component of v is 8i.

Vectors:_________________


Part B:
Let vector u=<-2,-27>, vector v=<-4, -27>, and vector w=<5,5>. Find the vector x that satisfies 4u-v+x+9x+w.

In this case, vector x=_____________________
IMG_0456.jpg
 
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Christian. said:
Good afternoon
How do you do this problem? I don't know where to start. Thanks.
Click to expand...

You'll have to start with whatever you know. If you can't show any work at all, please tell us what you know about the subject. Do you know what ||v|| means? Do you know what the i component is? Can you sketch what the vectors fitting the description might look like? Give us anything that can give us a starting point to help you.

Similarly, for the second, what is 4u + v, for example? And if vector x is <x,y>, what would the i component of each side of the equation be?
 
I know that ||v|| is the symbol for finding the norm of a vector, in this can vector V. The i component is the x component and j is the y component. I confused on how to sketch the graph.
 
Christian. said:
I don't know where to start on this problem. Need some hints. Thanks.
Part A:Find all vectors V in 2 dimensions having ||v||=17 where the i- component of v is 8i.

Part B:Let vector u=<-2,-27>, vector v=<-4, -27>, and vector w=<5,5>. Find the vector x that satisfies 4u-v+x+9x+w.
Click to expand...

A. Can you solve \(\displaystyle \sqrt{8^2+y^2}=17~?\) Can you explain why that works?
 
Christian. said:
I know that ||v|| is the symbol for finding the norm of a vector, in this can vector V. The i component is the x component and j is the y component. I confused on how to sketch the graph.
Click to expand...

Well, I want to see what you know (not just a list of things you know); for example, how do you actually find ||v||?

I can see better if you try doing some of the work.

The problem says,

Find all vectors v in 2 dimensions having ||v|| = 17 where the i-component of v is 8i.
​

(I'm using bold to represent a letter with an arrow over it.)

In the form v = <x,y>, what can you fill in?

What is the norm of this v?

How can you solve for what you didn't fill in?

Sketching is not necessary, but you should be learning to do it, so trying here will help. Give it a try! Make a pair of axes, and just draw in an arrow for v (don't try to do it correctly yet). What do you know about this arrow? How long should it be? Where should its head be? Now erase the arrow you drew and fix it so it fits these requirements.

The way you learn something new is by trying! Don't expect to understand everything before you do anything yourself; be bold (at least a little).
 
Using the distance formula to find the norm, I got the Vector point <8,15> which I think is the head. I know the magnitude is 17. I now have half of the vector.

FullSizeRender.jpg
 
I now understand part A, and I figured out part B. Just a little algebra. Thank you everyone who helped me.

IMG_0460.jpg
 
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Christian. said:
Using the distance formula to find the norm, I got the Vector point <8,15> which I think is the head. I know the magnitude is 17. I now have half of the vector.
Click to expand...

Good: the norm is 17, so 8^2 + y^2 = 17^2, and y = 15. Except that there are two solutions; y = -15 works also. (Always remember when solving an equation by taking a square root, that there are two roots.)

Is that what you mean by "I now have half the vectors", or do you think that <8,15> is not the answer?

Your graph shows another vector, with its tail at (0,-2). What is that for? That vector would have magnitude (norm) sqrt(8^2 + 17^2) = sqrt(353) = 18.788. The vector <8,15> has its tail at (0,0) and head at (8,15), which is how we draw any vector unless there is reason to do otherwise. Note that <8,15> denotes a vector, and (8,15) is a point. The vector's components are the horizontal and vertical distances from the tail to the head.

We may need to discuss this further, or rereading your book may clarify these ideas. Once you have it clear, try the second problem.
 
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