Help with component form of a vector

[winniethemath]

Hello I wanted to know if someone could explain how to find the component form of the vector V. The
Magnitude of v: ?v? = 12 and the direction of v: u = 〈3, −5〉

 

[LCKurtz]

Hello I wanted to know if someone could explain how to find the component form of the vector V. The
Magnitude of v: ?v? = 12 and the direction of v: u = 〈3, −5〉

Make a unit vector out of [MATH]\vec u[/MATH] and multiply it by [MATH]12[/MATH].

 

[Steven G]

I wouldn't even bother finding the unit vector. Where are you have trouble? Do you know how to compute the magnitude of a vector. Do you know how to change the magnitude of a vector without changing its direction?

 

[Otis]

I wouldn't even bother finding the unit vector …

Hey Jomo. Winnie may be learning introductory vector methods in a calculus course. If so, then Kurtz's approach is probably what's expected.

Were you thinking about using similar triangles? (Writing and solving proportions would take roughly the same amount of effort, I suspect.)

?

 

[Steven G]

If vector u had a magnitude of m, then I would just compute (12/m)u to solve the OPs problem.

 

[pka]

Hello I wanted to know if someone could explain how to find the component form of the vector V. TheMagnitude of v: ?v? = 12 and the direction of v: u = 〈3, −5〉

\(\vec{\bf{v}}=\dfrac{12}{\|\vec{\bf{u}}\|}\vec{\bf{u}}\)

 

[LCKurtz]

Aren't all the followup posts just rewording the suggestion I gave?

 

[Otis]

If vector u had a magnitude of m, then I would just compute (12/m)u …

Hi Jomo. The value of m is not given, so you would need to determine it, before dividing by it. And those two steps are equivalent to what Kurtz suggested.

 

[Steven G]

Hi Jomo. The value of m is not given, so you would need to determine it, before dividing by it. And those two steps are equivalent to what Kurtz suggested.

I was just hinting to the OP that it is an easy problem and that the easy method that Kurtz mentioned could be made even easier. I did not mean anything more than that.

 

[Otis]

… the easy method that Kurtz mentioned could be made even easier …

I don't see that, but, okay.

\(\;\)

 

[Steven G]

I don't see that, but, okay.

\(\;\)

In both methods you have to find the magnitude of u. Then using Kurtz method you compute u/||u|| and then multiple u/||u|| by 12. In my method I was just saying that after you have ||u|| then multiply u by (12/||u||).

It is similar to solving \(\displaystyle \dfrac{2}{5}x = 9\). You can multiply by 5 and then dividing by 2 OR you could have just multiplied by 5/2.

 

[Otis]

… You can multiply by 5 and then [divide] by 2 OR you could [just multiply] by 5/2.

Ah, I see we have a different perspective. As far as "made much easier" is concerned, those two look equivalent to me.

 

[winniethemath]

Make a unit vector out of [MATH]\vec u[/MATH] and multiply it by [MATH]12[/MATH].

Thanks! I tried watching many videos but I am having trouble because the 5 is negative so I would get square root of negative 16. I don't quite understand how to proceed.

 

[winniethemath]

Hey Jomo. Winnie may be learning introductory vector methods in a calculus course. If so, then Kurtz's approach is probably what's expected.

Were you thinking about using similar triangles? (Writing and solving proportions would take roughly the same amount of effort, I suspect.)

?

Yes it is the first time we review this! Thanks!

 

[Steven G]

Note that (3)^2 + (5)^2 = 9 + 25 = 34 AND (3)^2 + (-5)^2 = 9 + 25 = 34 give the same answer.

(-5)^2 = (-5)*(-5) = 25 NOT -25

For completeness note that -5^2 = - 5*5 = -25

 

[winniethemath]

Note that (3)^2 + (5)^2 = 9 + 25 = 34 AND (3)^2 + (-5)^2 = 9 + 25 = 34 give the same answer.

(-5)^2 = (-5)*(-5) = 25 NOT -25

For completeness note that -5^2 = - 5*5 = -25

Thank you so much!!!!

 

[Steven G]

Thank you so much!!!!

So what answer are you getting?

BTW, are you really in a Calculus class?

 

[winniethemath]

So what answer are you getting?

BTW, are you really in a Calculus class?

Lol its pre calculus I just had a brain fart there. I got 11.64 but I do not believe it is correct.

 

[Steven G]

Lol its pre calculus I just had a brain fart there. I got 11.64 but I do not believe it is correct.

Of course it is not correct. V is a multiple of u. u= <3,-5>. Any multiple of u would be in the form of < some number, some number>.
Your answer of 11.64 is not in the correct form and therefore must be wrong. It is just a single number.

 

[Otis]

… I got 11.64 …

Hi winnie. What is that number? They asked for the two components of vector v.

A unit vector has length 1. We get the unit vector for u by dividing each of its components by its magnitude. Multiply that unit vector by 12, and you will have the compnents of vector v.

?