how to find vector components from magnitude and angle This is a topic that many people are looking for. savegooglewave.com is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, savegooglewave.com would like to introduce to you How To Find The Vector Components Given The Magnitude and Direction Angle. Following along are instructions in the video below:
This lesson. What were going to do is find the components of a vector vector given the magnitude and the direction angle of that vector so lets draw picture first. So we have vector v.
Which im going to draw it in red. And it has a magnitude of 8. And an angle of 30 degrees with respect to the x axis.
So what are the components of vector v. So v. Is represented by the hypotenuse of this triangle.
Its composed of an x component and a y component. So to represent v income in component. Form.
Rather. The x component. Is going to be v.
Times. Cosine beta. And the y component.
Is going to be v. Times. Sine theta.
Where v. Is the magnitude of the vector.
So in this example is going to be 8 cosine. 30. 8.
Sine. 30. Now what is cosine.
30. Cosine. 30.
Is basically the square root of 3 over 2 sine. 30 is 1 2. So 8 divided by 2 is 4.
So its 4 square root. 3 comma. 4.
So if you were to draw a picture. This is 8 this is 4 root. 3.
And that this is 4 now you can check to see if you have the right answer. Lets calculate the magnitude using. These numbers.
Its going to be the square root of 4 square root. 3.
Squared plus 4. Squared. 4.
Squared is 16 square root. 3. Squared is history 16 times.
3. Is 48 and 48 plus. 16.
Is 64. The square root of 64 is 8. Which gives us the original magnitude so we know that this answer is correct.
Now thats only one way in which you could represent the vector you can also write the vector this way for square root. 3. I plus 4 j.
So you can also use the unit vectors. I and j to represent a vector now lets work on another example for the sake of practice. What are the components of vector w.
Which has a magnitude of 12 and a direction angle of 130 degrees. So feel free to pause. The video and try this example.
So we have the magnitude and we have the angle. So lets represent the vector in component form using the unit vectors.
I and j so w. Is going to be the magnitude times cosine times the unit vector i plus the magnitude times sine times the unit vector j. So its gonna be 12 cosine of 130 degrees plus.
12. Sine 130 degrees. Times j.
So. Make. Sure your calculator is in degree mode.
12. Cosine. 130 is basically negative seven point seven one and then times.
The unit vector i 12 times sine 130 is positive nine point one nine times unit vector j. So this right here is the answer now lets make sense of this answer in what quadrant is this vector located would you say its in quadrant. One two or three or quadrant four now notice that the x component is negative x is negative on the left side the y component is positive so this vector has to be in quadrant two and looking at the angle.
That makes sense quadrant. 2. Is between 90 degrees.
And 180 degrees. And 130 fits that description so an angle of 130 will give us a negative x component and a positive y component. And so these are little things that you can take a look at to make sure that your answer is correct.
So thats basically it for this video. If you liked it dont forget to subscribe and hit that like button thanks for watching. .
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