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Math Help - Vectors

  1. #1
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    Vectors

    If |x|=13, |y|=17 and |x+y|=45, find |x-y|

    x and y are both vectors

    My answer is
    (-1109)^0.5

    i want to know if this is correct
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  2. #2
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    Quote Originally Posted by skeske1234 View Post
    If |x|=13, |y|=17 and |x+y|=45, find |x-y|
    x and y are both vectors
    This is an impossible problem. See the red above.
    45 = \left\| {x + y} \right\| \leqslant \left\| x \right\| + \left\| y \right\| = 13 + 17.
    Do you see any thing wrong with that?
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  3. #3
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    x and y are bigger than x-y .......
    so they have a typo....
    what should i write as an answer then?
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  4. #4
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    Quote Originally Posted by skeske1234 View Post
    x and y are bigger than x-y .......
    so they have a typo....
    what should i write as an answer then?
    I would put that there is no answer possible.
    I suspect they meant 25 = \left\| {x + y} \right\|
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  5. #5
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    Assuming that it was really |x+y|= 25, then, by the "parallelogram rule" for vector addtion, x+ y is the one diagonal of a parallelogram having sides x and y and x- y is the other diagonal. You can find the angle in the triangle with sides x, y, and x+y by using the cosine law on a triangle with sides of length 25, 13, and 17, then use the cosine law on a triangle with sides x, y, and x- y, and the same angle, to find the length of x-y.

    Or you could use the fact that |x+y|= \sqrt{(x+y)\cdot(x-y)} = \sqrt{x\cdot x+ 2x\cdot y+ y\cdot y}= 25 to argue that x\cdot x+ 2 x\cdot y+ y\cdot y= 25^2= 625. You can easily find x\cdot x and y\cdot y and then find 2x\cdot y. Now use the fact that (x-y)\cdot(x-y)= x\cdot x- 2 x\cdot y+ y\cdot y to find |x-y|.

    In fact, do it both ways, as a check and really shock your teacher!
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  6. #6
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    Quote Originally Posted by HallsofIvy View Post
    Assuming that it was really |x+y|= 25, then, by the "parallelogram rule" for vector addtion, x+ y is the one diagonal of a parallelogram having sides x and y and x- y is the other diagonal. You can find the angle in the triangle with sides x, y, and x+y by using the cosine law on a triangle with sides of length 25, 13, and 17, then use the cosine law on a triangle with sides x, y, and x- y, and the same angle, to find the length of x-y.
    Or you could use the fact that |x+y|= \sqrt{(x+y)\cdot(x-y)} = \sqrt{x\cdot x+ 2x\cdot y+ y\cdot y}= 25 to argue that x\cdot x+ 2 x\cdot y+ y\cdot y= 25^2= 625. You can easily find x\cdot x and y\cdot y and then find 2x\cdot y. Now use the fact that (x-y)\cdot(x-y)= x\cdot x- 2 x\cdot y+ y\cdot y to find |x-y|.
    On a much simpler level. It is well known that:
    \left\| {x + y} \right\|^2  + \left\| {x - y} \right\|^2  = 2\left\| x \right\|^2  + 2\left\| y \right\|^2 .
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