What represents the vector: 2a-5b

  1. 1. The problem statement, all variables and given/known data

    if vector :

    line a starts from co-ordinates (0,0) and ends at (5,3)

    line b starts from co-ordinates (0,0) and ends at (1,2)

    What represents the vector: 2a-5b

    2. Relevant equations



    3. The attempt at a solution

    I was initially thinking of computing Pythagorus theorem for each of the two lines.

    for Line a = square root of (25+9) = square root of 24
    for line b = square root of (1+4) = square root of 5

    2a-5b = 2 x square root of 6 - 5 x square root of 5

    which doesn't seem right...tips would be nice please.

    need an answer in the form of an x and y co-ordinate
     
  2. jcsd
  3. Not sure of what 2a means. Does it mean a vector starting at (0,0) and ending at
    (10,6)? Does 5b mean a vector starting at (0,0) and ending at (5,10)?
     
  4. anyone else? tips or hints?
     
  5. ehild

    ehild 12,458
    Homework Helper
    Gold Member
    2014 Award

    2a means twice the vector a, a vector in the same line as a and of twice length. In coordinates, a=(5,3) and the vector is represented by an arrow starting at (0,0) and ending at (5,3). 2a=(10,6), 5b=(5,10)
    2a-5b means the difference between 2a and 5b. When you add (subtract) vectors, you add (subtract) the components.

    ehild
     
  6. HallsofIvy

    HallsofIvy 40,960
    Staff Emeritus
    Science Advisor

    Most importantly, there is nothing here that asks you to find the length of any vector. Do not use the Pythagorean theorem!
     
  7. so if 2a=(10,6), 5b=(5,10)

    and 2a-5b

    then

    10-5 = 5

    6-10 = -4

    therefore= 2a-5b=(5,-4)
     
  8. thanks guys especially echild- whats your qualifications?
     
  9. ehild

    ehild 12,458
    Homework Helper
    Gold Member
    2014 Award

    You are welcome.

    ehild
     
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