Vector Direction Help: Solving a Vector Problem with Given Direction and Length

In summary, the conversation is about finding the components of vector u given its direction and a specific relationship with vector v. The steps to solve the problem include writing v in the form v = ___ i + ___ j, using the relationship 3|u| = 2|v|, and finding the components of u using the magnitude of v. The conversation ends with the person understanding how to solve the problem.
  • #1
teffy3001
23
0
ive been trying to do this problem but i don't know where to start...any help?


let v be a vector of length 9 in the direction 65degrees south of west.

if u has the same direction as v, and if 3|u| = 2|v|, then which of the following can be used to describe u?


u = 5.705i + 12.235j
u = -2.536i - 5.438j
u = 2.536i + 5.438j
u = -5.705i - 12.235j
none of these
 
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  • #2
teffy3001 said:
none of these

Are you sure about that?
 
  • #3
no I am not sure...cause I am not even sure how to get started on this question...
 
  • #4
teffy3001 said:
no I am not sure...cause I am not even sure how to get started on this question...

Draw your vector v down, first. Do you know anything about projections on the x and y axis?
 
  • #5
yeah
i think i have to find the components of u but using the magnitude of v..is that right?
 
  • #6
teffy3001 said:
yeah
i think i have to find the components of u but using the magnitude of v..is that right?

First of all, you have to write down v in the form v = ___ i + ___ j. Then, you know that 3|u| = 2|v|, eg |u| = 2/3|v|.
 
  • #7
okay thanks i think i got it now : )
 

1. What is a vector?

A vector is a mathematical quantity that has both magnitude (size) and direction. It is often represented as an arrow pointing in a specific direction, with the length of the arrow representing the magnitude of the vector.

2. How do you determine the direction of a vector?

The direction of a vector can be determined by using either the angle it makes with a known reference axis (such as the x-axis), or by using the components of the vector in the x and y direction.

3. Can vectors have negative direction?

Yes, vectors can have negative direction. This means that the vector is pointing in the opposite direction of the reference axis. For example, a vector pointing in the negative x-direction would have a negative x-component.

4. How do you add or subtract vectors with different directions?

To add or subtract vectors with different directions, you must first determine the components of each vector in the same reference axis. Then, you can add or subtract the components to get the resulting vector in the same reference axis. Finally, you can use the components to determine the magnitude and direction of the resulting vector.

5. What is the difference between vector direction and vector magnitude?

Vector direction refers to the orientation or angle at which a vector is pointing, while vector magnitude refers to the size or length of the vector. Both direction and magnitude are necessary to fully describe a vector.

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