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

AI Thread Summary
To find the magnitude of vector C in the equation A + B + C = 0, where vector A has a magnitude of 3 to the right and vector B has a magnitude of 4 upwards, vector C must point left and downwards. The correct approach involves determining the components of vectors A and B, which combine to point up-right, necessitating a vector C that counters this direction. The magnitude of vector C is calculated as 5, derived from the Pythagorean theorem using the components of A and B. This ensures that the sum of the vectors equals zero, confirming the balance in the vector equation.
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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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Draw a picture.
 
What SteamKing said. It's not 6.4
 
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?
 
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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Chestermiller said:
Where did the "5" come from?

It should be 3^2. Careless blunder
 
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
 
negation said:
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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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:

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 :)
 
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