Vector Addition? Which Vectors Do I Draw and Where?

In summary, using the Cosine and Sine Laws, it is possible to determine the magnitude and direction of 5a - 2b by breaking down the vectors into their components and adding them together. It is important to choose a consistent approach when determining the direction and angle, as using different drawings may result in different results.
  • #1
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Homework Statement


Vectors a and b have magnitudes 2 and 3. The angle between them is 50 degrees. Determine 5a - 2b and determine its magnitude and direction


Homework Equations


Cosine Law and Sine Law



The Attempt at a Solution


I can solve for the magnitude using the cos law and obtain an answer of 7.67 which is correct, however the direction and angle looks as if which vector i draw and where I draw it Heres a picture (The magnitudes I have just labelled as 10 which is 5a and 6 for 2b) :

Untitled_zpsd4cc7bd5.png


Which drawing should I use, because It results in me getting different angles and direction
 
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  • #2
The most straightforward approach would be to pick one vector as the x axis, then break the other into its component, and add them that way.
 

FAQ: Vector Addition? Which Vectors Do I Draw and Where?

How do I add two vectors?

To add two vectors, you must first determine their magnitude and direction. Then, you can use the head-to-tail or parallelogram method to draw the vectors and find the resultant vector. The resultant vector represents the sum of the two original vectors.

Which vectors do I draw when adding more than two vectors?

When adding more than two vectors, you must draw all the given vectors and arrange them in a head-to-tail or parallelogram configuration. The resultant vector will be drawn from the tail of the first vector to the head of the last vector.

Can I add vectors with different units?

No, you cannot add vectors with different units. Vectors must have the same units in order to be added. If they have different units, you must convert them to the same unit before adding them.

Where do I draw the resultant vector?

The resultant vector is drawn from the tail of the first vector to the head of the last vector. If using the head-to-tail method, the resultant vector is drawn from the tail of the first vector to the head of the last vector. If using the parallelogram method, the resultant vector is drawn from the intersection of the two vectors to the opposite corner of the parallelogram.

What is the difference between adding vectors algebraically and graphically?

Adding vectors algebraically involves finding the sum of the individual components of the vectors in the x and y direction. Graphically, adding vectors involves drawing the vectors and finding the resultant vector. Both methods will result in the same magnitude and direction of the resultant vector.

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