What is the magnitude of vector C in a balanced vector equation?

In summary, to find the magnitude of vector C such that A + B + C = 0, we can use the Pythagorean theorem to calculate the magnitude of vector C, which is equal to the square root of the sum of the squares of the magnitudes of vectors A and B. We can also use the concept of vector components to determine the direction and magnitude of vector C. Finally, we can solve for the magnitude of vector C by setting the sum of vectors A, B, and C equal to 0.
  • #1
negation
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0

Homework Statement



Vector A has magnitude 3 and points to the right. Vector B has magnitude 4 and points vertically upwards. Find the magnitude of vector C such that A + B + C = 0


The Attempt at a Solution



C = SQRT[4^2 + 5^2] = 6.4
 
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  • #2
Draw a picture.
 
  • #3
What SteamKing said. It's not 6.4
 
  • #4
negation said:

Homework Statement



Vector A has magnitude 3 and points to the right. Vector B has magnitude 4 and points vertically upwards. Find the magnitude of vector C such that A + B + C = 0


The Attempt at a Solution



C = SQRT[4^2 + 5^2] = 6.4
Where did the "5" come from?
 
  • #5
Very good idea to draw a picture as SteamKing said.

Another approach is to express the direction of the vectors with ##\hat{i}## and ##\hat{j}## components, where ##\hat{i}## represents the x-direction of the vector and ##\hat{j}## represents the y-direction of the vector.

Here is the concrete demonstration of the vectors: if a vector points to the right, then we obtain the positive ##\hat{i}## component. If a vector points up, then we obtain the positive ##\hat{j}## component. From here, we see that if a vector points up and right, then we obtain both positive ##\hat{i}## and ##\hat{j}## components.

Remember, when combining vectors, you have to add their magnitudes component-wise as you do with variables in pre-calculus class.

Note: The combination of those two vectors don't give you the answer you want since it points up-right. You need to figure out the vector ##\vec{C}## in which ##\vec{A} + \vec{B} + \vec{C} = 0##
 
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  • #6
Chestermiller said:
Where did the "5" come from?

It should be 3^2. Careless blunder
 
  • #7
steamking said:
draw a picture.

nasusama said:
very good idea to draw a picture as steamking said.

Another approach is to express the direction of the vectors with ##\hat{i}## and ##\hat{j}## components, where ##\hat{i}## represents the x-direction of the vector and ##\hat{j}## represents the y-direction of the vector.

Here is the concrete demonstration of the vectors: If a vector points to the right, then we obtain the positive ##\hat{i}## component. If a vector points up, then we obtain the positive ##\hat{j}## component. From here, we see that if a vector points up and right, then we obtain both positive ##\hat{i}## and ##\hat{j}## components.

Remember, when combining vectors, you have to add their magnitudes component-wise as you do with variables in pre-calculus class.

Note: The combination of those two vectors don't give you the answer you want since it points up-right. You need to figure out the vector ##\vec{c}## in which ##\vec{a} + \vec{b} + \vec{c} = 0##

Capture.JPG
 
  • #8
negation said:
View attachment 65462
Your C vector has two heads. It should only have one. Which one do you judge is the correct one?
Chet
 
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  • #9
Chestermiller said:
Your C vector has two heads. It should only have one. Which one do you judge is the correct one?
Chet

The correct one points to the left.
 
  • #10
negation said:
View attachment 65462

The vector ##\vec{C}## does NOT point to the right. As I mentioned before:

The combination of those two vectors don't give you the answer you want since it points up-right. You need to figure out the vector ##\vec{C}## in which ##\vec{A} + \vec{B} + \vec{C} = 0##

negation said:
The correct one points to the left.

Good. Also, which ##y##-direction is the vector ##\vec{C}## pointing at? Remember that its direction is opposite to the combination of the two vectors ##\vec{A}## and ##\vec{B}##, which points up-right. The vector ##\vec{C}## does not only point to the left. It also points... (You figure out the y-direction)
 
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  • #11
NasuSama said:
The vector ##\vec{C}## does NOT point to the right. As I mentioned before:

The combination of those two vectors don't give you the answer you want since it points up-right. You need to figure out the vector ##\vec{C}## in which ##\vec{A} + \vec{B} + \vec{C} = 0##



Good. Also, which ##y##-direction is the vector ##\vec{C}## pointing at? Remember that its direction is opposite to the combination of the two vectors ##\vec{A}## and ##\vec{B}##, which points up-right. The vector ##\vec{C}## does not only point to the left. It also points... (You figure out the y-direction)

It also points downwards. It is in the direction -j hat
 
  • #12
Nicely done. ;) Finally, determine the magnitude of ##\vec{C}##, and you are done.
 
  • #13
NasuSama said:
Nicely done. ;) Finally, determine the magnitude of ##\vec{C}##, and you are done.

Magnitude of c = 5
 
  • #14
yep :)
 

Related to What is the magnitude of vector C in a balanced vector equation?

1. What is a vector?

A vector is a mathematical quantity that has both magnitude (size) and direction. It is represented by an arrow pointing in the direction of the vector with a length proportional to its magnitude.

2. How is a vector different from a scalar?

A scalar is a mathematical quantity that has only magnitude, such as temperature or mass. A vector, on the other hand, has both magnitude and direction.

3. How do you add two vectors?

To add two vectors, you can use the head-to-tail method or the parallelogram method. In the head-to-tail method, you place the tail of the second vector at the head of the first vector, and the resultant vector is drawn from the tail of the first vector to the head of the second vector. In the parallelogram method, you draw the two vectors from a common point, and the resultant vector is the diagonal of the parallelogram formed by the two vectors.

4. What is the difference between a position vector and a displacement vector?

A position vector describes the location of a point in space relative to the origin, while a displacement vector describes the change in position of an object from its initial position to its final position.

5. What is the magnitude of a vector?

The magnitude of a vector is its size or length. It is calculated using the Pythagorean theorem, where the magnitude is equal to the square root of the sum of the squares of its components (x and y for a 2-dimensional vector, or x, y, and z for a 3-dimensional vector).

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