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Math Help - Vectors problem

  1. #1
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    Question Vectors problem

    a and b are two position vectors of two distinct points A and B , neither of which is the origin. show that if (modulus) a+b = (modulus) a-b , then a is perpendicular to b using :
    a. a vector algebraic method
    b. a geometric argument

    I don't quite understand what they mean by these^
    I've drawn a quick diagram using word, see image below.
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  2. #2
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    Re: Vectors problem

    Quote Originally Posted by kandyfloss View Post
    a and b are two position vectors of two distinct points A and B , neither of which is the origin. show that if (modulus) a+b = (modulus) a-b , then a is perpendicular to b using :
    a. a vector algebraic method
    b. a geometric argument
    For part a), recall that \|a\pm b\|^2=(a\pm b)\cdot (a\pm b).

    For part b), what type of quadrilateral diagonals of equal lengths?
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  3. #3
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    Re: Vectors problem

    part a) oh yeah, i agree on that rule. but how does it help me explain a is perpendicular to b?
    part b) parallelogram ?
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  4. #4
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    Re: Vectors problem

    Quote Originally Posted by kandyfloss View Post
    part a) oh yeah, i agree on that rule. but how does it help me explain a is perpendicular to b?
    part b) parallelogram ?
    You are given that \|a+b\|=\|a-b\| squaring we get
    (a+b)\cdot(a+b)=(a-b)\cdot(a-b).
    Expand to see what happens.
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  5. #5
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    Re: Vectors problem

    Ok, thanks. and about the part b) since it's a parallelogram the diagonals intersect at 90 deg and adjacent sides are perpendicular to each other. right?
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