Vectors and magnitudes

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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SteamKing
Staff Emeritus
Homework Helper
Draw a picture.

CWatters
Homework Helper
Gold Member
What SteamKing said. It's not 6.4

Chestermiller
Mentor

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##

1 person
Where did the "5" come from?
It should be 3^2. Careless blunder

draw a picture.
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##

Chestermiller
Mentor
Your C vector has two heads. It should only have one. Which one do you judge is the correct one?
Chet

1 person
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.

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##

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)

1 person
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

Nicely done. ;) Finally, determine the magnitude of ##\vec{C}##, and you are done.

Nicely done. ;) Finally, determine the magnitude of ##\vec{C}##, and you are done.
Magnitude of c = 5

BruceW
Homework Helper
yep :)