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Math Help - Find vectors b1 and b2

  1. #1
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    Find vectors b1 and b2

    Two vectors a = 2i - 2j +k and b = 2i + j - k are given. Write the vector b as sum of vectors \mathbf{b_1} and \mathbf{b_2} such that \mathbf{b_1} is parallel to a and \mathbf{b_2} is perpendicular to a.Find the vectors \mathbf{b_1} and \mathbf{b_2}
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  2. #2
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    Quote Originally Posted by varunnayudu View Post
    Two vectors a = 2i - 2j +k and b = 2i + j - k are given. Write the vector b as sum of vectors \mathbf{b_1} and \mathbf{b_2} such that \mathbf{b_1} is parallel to a and \mathbf{b_2} is perpendicular to a.Find the vectors \mathbf{b_1} and \mathbf{b_2}
    b = b1 + b2

    Well b1 is parallel to a is the same as saying b1 = za.
    b2
    is perpendicular to a is same as saying b2 . a = 0.

    From b = b1 + b2 we get, b.a = b1 . a = z |a|^2 you can get z and thus b1.

    Then you can get b2 by b - b1.

    Get it?
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