math

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if a & b are perpendicular vectors, show that
a)(a+2b).(a-b)=|a|^2-2|b|^2
b)(a+b).(a-b)=|a|^2+|b|^2

*how to show it?just multiply it?if yes where does||come from?
does||show that it should be a value?

  • math -

    | | around a number means "magnitude of". You will need to use the following relationships:
    a*a = |a|^2
    b*b = |b|^2
    a*b = 0, because they have said that a and b are perpendicular.

    Th "*" operator means "dot product", which I assume you have learned the meaning of. In general, for vectors x and y,
    x*y = |x| |y| cos(theta)
    where theta is the angle between the two vectors. Thus, in this case,

    a) (a+2b)*(a-b)=
    a*a -a*b + 2b*a -2b*b

    |a|^2 - 2|b|^2

    Do problem (b) the same way.

  • math (clarification) -

    My first line should have read:

    | | around a number VECTOR means magnitude of that vector

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