How to determine what vector A is equal to?

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In summary: Thank you for your help!In summary, the given equations state that A+B equals 2C and B-2A equals -C. If C is equal to 1i + 2j + 3k, vector A is equal to vector C. By combining the equations, it is possible to eliminate B and solve for the relationship between A and C.
  • #1

Homework Statement


Three vectors are related as by the equations: A+B = 2C and B-2A = -C.
If C= 1i + 2j +3k then what is vector A equal to?

Homework Equations


i, j, and k are unit vectors

The Attempt at a Solution


The solution in my answer key says that vector A = vector C but I don't understand how they arrived at that. Any clarification would be appreciated, thanks!
 
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  • #2
Hi eng, :welcome:

A bit awkward if the template asks for relevant eqations, right ? You still need something there. The statement that ##\hat\imath, \hat \jmath, \hat k## are unit vectors is nice to form an idea, but it doesn't help solve the equations...

If A, B and C were numbers, how would you solve A+B = 2C & B-2A = -C ?
 
  • #3
BvU said:
Hi eng, :welcome:

A bit awkward if the template asks for relevant eqations, right ? You still need something there. The statement that ##\hat\imath, \hat \jmath, \hat k## are unit vectors is nice to form an idea, but it doesn't help solve the equations...

If A, B and C were numbers, how would you solve A+B = 2C & B-2A = -C ?

Hi! Thanks for taking a look at my question and if they were numbers would I combine the 2 equations? A's and B's on one side with C's on the other and get A-2A + B+B = 2C-C (simplified: -A +2B = C)?
 
  • #4
engphys204 said:
Hi! Thanks for taking a look at my question and if they were numbers would I combine the 2 equations? A's and B's on one side with C's on the other and get A-2A + B+B = 2C-C (simplified: -A +2B = C)?
You are looking for a relationship between A and C. So you need to combine the equations in a way which ... does what?
 
  • #5
haruspex said:
You are looking for a relationship between A and C. So you need to combine the equations in a way which ... does what?
something that eliminates the B from the equation? Subtract them?
 
  • #6
engphys204 said:
something that eliminates the B from the equation? Subtract them?
Of course.
 
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  • #7
haruspex said:
Of course.
ohhh thanks I got it!
 

What is a vector?

A vector is a mathematical quantity that has both magnitude and direction. It is typically represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.

How do vectors differ from scalars?

Vectors differ from scalars in that scalars only have magnitude, while vectors have both magnitude and direction. Examples of scalars include temperature and time, while examples of vectors include displacement and velocity.

How do you determine the magnitude of a vector?

The magnitude of a vector can be found using the Pythagorean theorem, where the magnitude is equal to the square root of the sum of the squares of the vector's components. Alternatively, if the vector is given in component form, the magnitude can be found by taking the square root of the sum of the squares of the components.

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

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

How do you add or subtract vectors?

To add or subtract vectors, you can use the parallelogram method or the head-to-tail method. For the parallelogram method, draw the vectors as adjacent sides of a parallelogram, and the diagonal of the parallelogram will represent the resultant vector. For the head-to-tail method, draw the first vector, and then draw the second vector starting from the end of the first vector. The resultant vector is the vector from the beginning of the first vector to the end of the second vector.

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