Vector Linear Combinations: Solving for Scalar Quantity

In summary, the conversation discussed finding the linear combination of two vectors, one directed at an angle of 45 degrees with a magnitude of square root of 2, and the other directed at an angle of 150 degrees with a magnitude of 6. The individual attempted to find the scalar quantity but was not successful and asked for help. They were then given a hint to find a unit vector and multiply by the magnitude, along with suggestions for websites to use as tutorials. Eventually, they were able to figure out the solution.
  • #1
Hollysmoke
185
0
The question is to write the following vectors as a linear combination:

c) a vector directed at an angle of 45 degrees with a magnitude of square root of 2.

d)a vector directed at an angle of 150 degrees with a magnitude of 6.

What I tried to do is to find the scalar quantity with the vector but I'm not getting a right answer. Could someone please help me in the right direction?
 
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  • #2
As a linear combination of what?
 
  • #3
oh sorry. i+j
 
  • #4
i and j. not i+j.
 
  • #5
does anyone know any website that I could use as a tutorial, then?
 
  • #6
Hint:First find a unit vector in the given direction using direction cosines.
Then multiply by magnitude.
 
  • #8
Thank you for the websites and thank you for the help. I figured it out with that hint :D
 

1. What is a vector linear combination?

A vector linear combination is a mathematical operation where two or more vectors are added or subtracted to create a new vector. This new vector is a combination of the original vectors and is determined by the scalars (numbers) used to multiply each vector before adding them together.

2. How do you solve for the scalar quantities in a vector linear combination?

To solve for the scalar quantities in a vector linear combination, you must set up a system of equations using the given vectors and their corresponding scalars. Then, use algebraic methods to solve for the values of the scalars.

3. What is the purpose of solving for scalar quantities in a vector linear combination?

The purpose of solving for scalar quantities in a vector linear combination is to determine the specific combination of vectors that will result in a desired outcome. This is commonly used in physics and engineering to find the optimal direction and magnitude of forces.

4. Can you have more than two vectors in a linear combination?

Yes, you can have any number of vectors in a linear combination. The process of solving for the scalar quantities remains the same, but the number of equations needed will increase with each additional vector.

5. Are there any properties or rules that apply to vector linear combinations?

Yes, there are a few properties and rules that apply to vector linear combinations. These include the commutative property (order of addition does not matter), the associative property (bracketing of vectors does not matter), and the distributive property (scalar can be factored out of the vector combination).

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