I used my calculator to answer these questions. Is there any way to solve these without a calculator?

I went to high school with trig tables, log tables and a slide rule. Why would anyone not want to us a calculator!

I try using the google calculator and I keep getting slightly different results... in the first one, instead of -2.85 and 10.63 I kept getting -2.65 and 10.68. I realy kept trying and retrying, checking and rechecking, and it still remained the same. Anyone else having this problem?

One thing you should check is to see what mode the calculator is in (radians or degrees) if you are in the wrong mode for the measure of angle you are using you will get the wrong answer. If that isn't the problem the only other issue I can think of would be troubles with rounding and/or significant figures. Hope this helps!

Hi, I'm working on some component form of vector questions right now and I understand how to find the components given magnitude and direction as Sal taught in the video. However, what I still don't understand is what the vector components give you... like what does that resultant vector mean? What is it? I would really appreciate it if someone could explain.

In physics if yoy have two forces pushing from different directions you can use vector addition to solve for the resulting force. For example, if you push a block of wood in one direction and your friend pushes at an angle, the block will go in the resultant direction.

if the resultant of 2 equal vectors is twice the magnitude of each of them what will be the angle between the 2 vectors?? THANKS

If the vectors are equal, they must have the same direction. So the angle between them is 0.

Law of sines works right?

Yes, but it takes more time, it is easier to use trig functions so x=cos(angle)*magnitude and y=sin(angle)*magnitude.

I was doing the 2nd question with x = 10*cos(-50), y = 10*sin(-50) is this correct approach?

Your approach is 95% correct except that in the fourth quadrant cosine is positive and sine is negative so vector u: -> u = _(10*cos(50),10*sin(-50))_

Main content

Course: Precalculus > Unit 6

Lesson 7: Vector components from magnitude and direction

Vector components from magnitude & direction (advanced)

Google Classroom

Find a vector's components from its magnitude and direction. Direction angle is not given directly.

Introduction

Each of the two problems below asks you to convert a vector from magnitude and direction form into component form.

But watch out! The direction angles aren't given for these vectors. You'll need to be careful what you plug into the sine and cosine functions.

Problem 1

The vector

\vec{v}

is shown below.

Find the component form of $\vec{v}$ ‍.
Round your final answers to the nearest hundredth.

\vec{v} \approx (

,

)

Finding the magnitude and direction angle.

The magnitude of

\vec{v}

11

The direction angle

θ

\vec{v}

is the angle between the positive

x

-axis and

\vec{v}

. The direction angle of

\vec{v}

180^{\circ} - 75^{\circ} = 105^{\circ}

To summarize:

$| | \vec{v} | | = 11$ ‍
$θ = 105^{\circ}$ ‍

Finding the $x$ ‍-component of $\vec{v}$ ‍

v_{x} = | | \vec{v} | | \cos (θ)

= 11 \cos (105^{\circ})

\approx - 2.85

Finding the $y$ ‍-component of $\vec{v}$ ‍

v_{y} = | | \vec{v} | | \sin (θ)

= 11 \sin (105^{\circ})

\approx 10.63

The answer

$\vec{v} \approx (- 2.85, 10.63)$ ‍

Does this answer make sense? Yes because

\vec{v}

is in the second quadrant. Any vector in the second quadrant must have a negative

x

-component and a positive

y

-component.

Problem 2

The vector

\vec{u}

is shown below.

What is the component form of $\vec{u}$ ‍?
Round your final answer to the nearest hundredth.

\vec{u} \approx (

,

)

Finding the magnitude and direction angle.

The magnitude of

\vec{u}

10

The direction angle

θ

\vec{u}

is the angle between the positive

x

-axis and

\vec{u}

. The direction angle of

\vec{u}

360^{\circ} - 50^{\circ} = 310^{\circ}

To summarize:

$| | \vec{u} | | = 10$ ‍
$θ = 310^{\circ}$ ‍

Finding the $x$ ‍-component of $\vec{u}$ ‍

u_{x} = | | \vec{u} | | \cos (θ)

= 10 \cos (310^{\circ})

\approx 6.43

Finding the $y$ ‍-component of $\vec{u}$ ‍

\begin{aligned} u_{y} & = | | \vec{u} | | \sin (θ) \\ = 10 \sin (310^{\circ}) \\ \approx - 7.66 \end{aligned}

The answer

$\vec{u} = (6.43, - 7.66)$ ‍

Does this answer make sense? Yes because

\vec{u}

is in the fourth quadrant. Any vector in the fourth quadrant must have a positive

x

-component and a negative

y

-component.

Want to join the conversation?

Sort by:

Jenna Sep
Posted 8 years ago. Direct link to Jenna Sep's post “I used my calculator to a...”
I used my calculator to answer these questions. Is there any way to solve these without a calculator?
Button navigates to signup pageComment on Jenna Sep's post “I used my calculator to a...”
(45 votes)
Answer
- willy nrobma
  Posted 8 years ago. Direct link to willy nrobma's post “I went to high school wit...”
  I went to high school with trig tables, log tables and a slide rule. Why would anyone not want to us a calculator!
  Comment on willy nrobma's post “I went to high school wit...”
  (107 votes)
anissa814
Posted 8 years ago. Direct link to anissa814's post “Hi, I'm working on some c...”
Hi, I'm working on some component form of vector questions right now and I understand how to find the components given magnitude and direction as Sal taught in the video. However, what I still don't understand is what the vector components give you... like what does that resultant vector mean? What is it? I would really appreciate it if someone could explain.
Button navigates to signup pageButton navigates to signup page
(4 votes)
Answer
- willy nrobma
  Posted 8 years ago. Direct link to willy nrobma's post “In physics if yoy have tw...”
  In physics if yoy have two forces pushing from different directions you can use vector addition to solve for the resulting force. For example, if you push a block of wood in one direction and your friend pushes at an angle, the block will go in the resultant direction.
  Button navigates to signup page
  (12 votes)
Roxanne Police
Posted 7 years ago. Direct link to Roxanne Police's post “I try using the google ca...”
I try using the google calculator and I keep getting slightly different results... in the first one, instead of -2.85 and 10.63 I kept getting -2.65 and 10.68. I realy kept trying and retrying, checking and rechecking, and it still remained the same. Anyone else having this problem?
Button navigates to signup pageComment on Roxanne Police's post “I try using the google ca...”
(5 votes)
Answer
- J E
  Posted 7 years ago. Direct link to J E's post “One thing you should chec...”
  One thing you should check is to see what mode the calculator is in (radians or degrees) if you are in the wrong mode for the measure of angle you are using you will get the wrong answer. If that isn't the problem the only other issue I can think of would be troubles with rounding and/or significant figures.
  Hope this helps!
  Comment on J E's post “One thing you should chec...”
  (7 votes)
Ejay Hall
Posted 7 years ago. Direct link to Ejay Hall's post “what is the component for...”
what is the component form of the vector 'a' with llall =100, 250 dg, approximate each component to the nearest tenth
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
Grace Yuan
Posted 8 years ago. Direct link to Grace Yuan's post “=||u⃗ ||cos(θ)should be ...”
=||u⃗ ||cos(θ)should be sin(θ) in the solution of Q2 Finding the y-component of vector u.
Button navigates to signup pageComment on Grace Yuan's post “=||u⃗ ||cos(θ)should be ...”
(3 votes)
Answer
Ana Conjuh
Posted 7 years ago. Direct link to Ana Conjuh's post “In my physics class, we s...”
In my physics class, we see the x and y axis inverted and turned in some problems, I have no idea what quadrant I'm in, how do I determine if (x,y) are pos/neg? Thanks
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- Chris O'Donnell
  Posted 7 years ago. Direct link to Chris O'Donnell's post “That's really strange. I'...”
  That's really strange. I've never seen anything like that before.
  Button navigates to signup page
  (1 vote)
Dream
Posted 7 years ago. Direct link to Dream's post “if the resultant of 2 equ...”
if the resultant of 2 equal vectors is twice the magnitude of each of them what will be the angle between the 2 vectors?? THANKS
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- kubleeka
  Posted 7 years ago. Direct link to kubleeka's post “If the vectors are equal,...”
  If the vectors are equal, they must have the same direction. So the angle between them is 0.
  Comment on kubleeka's post “If the vectors are equal,...”
  (2 votes)
Eric
Posted 7 years ago. Direct link to Eric's post “Law of sines works right?”
Law of sines works right?
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- Luis F. Vélez
  Posted 7 years ago. Direct link to Luis F. Vélez's post “Yes, but it takes more ti...”
  Yes, but it takes more time, it is easier to use trig functions so x=cos(angle)*magnitude and y=sin(angle)*magnitude.
  Button navigates to signup page
  (2 votes)
rishabh m
Posted 2 years ago. Direct link to rishabh m's post “I was doing the 2nd quest...”
I was doing the 2nd question with
x = 10*cos(-50), y = 10*sin(-50)
is this correct approach?
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- Nolan Ryzen Terrence
  Posted 2 years ago. Direct link to Nolan Ryzen Terrence's post “Your approach is 95% corr...”
  Your approach is 95% correct except that in the fourth quadrant cosine is positive and sine is negative so vector u:
  ->
  u = (10*cos(50),10*sin(-50))
  Button navigates to signup page
  (2 votes)
Hannah Lee
Posted 4 years ago. Direct link to Hannah Lee's post “I'm still confused on why...”
I'm still confused on why for some of the direction angles (in the first step) you would subtract them, but for the others you wouldn't subtract them.
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- Aiena
  Posted 4 years ago. Direct link to Aiena's post “Hi Hannah, Measure of th...”
  Hi Hannah,
  
  Measure of the angle is given to us indirectly.
  
  Always remember that the vector (looks like a ray) and the POSITIVE x-axis forms the angle.
  
  Since we are given 75 degrees as our angle, we subtract it from 180 degrees to get 105 degrees. This 75 degrees angle is formed with the vector and negative x-axis.
  
  I hope this helps.
  
  Aiena.
  Button navigates to signup page
  (1 vote)