What is the Value of s for Parallel Vectors in Linear Algebra?

In summary, the problem involves finding s for which the vectors (1-s)u - 2/3v and 3u + sv are parallel, given that u and v are linearly independent vectors. This can be solved algebraically by expressing parallelism in terms of a scalar and applying it to the two given vectors. The solution for s will determine if u and v are coplanar.
  • #1
byronsakic
17
0
the vectors u and v are linearly independent. find s, if vectors (1-s)u - 2/3v and 3u +sv are parallel.

where u and v are vectors.

i am totally clueless, even my tutor couldn't solve it.
 
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  • #2
How can you algebraically express that two vectors a and b are parallel?
Do that for the two vectors you are given (in function of s) and solve for s.
 
  • #3
but u and v are coplanar? XD
 
  • #4
Vectors a and b are parallel if there exists a scalair k such that a = kb. Apply that to the two vectors you want to be parallel, and find the s for which this holds.
 
  • #5
byronsakic said:
the vectors u and v are linearly independent. find s, if vectors (1-s)u - 2/3v and 3u +sv are parallel.
where u and v are vectors.
i am totally clueless, even my tutor couldn't solve it.

You might consider getting another tutor! :)
 

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