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Math Help - Vectors

  1. #1
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    Vectors

    p = 2i + 3j + 4k
    q = i + 3j + 2k
    r = 2i + j + ak

    If p.(q+r) is 6 greater than q.(p+r) find the value of a.

    This is what I've done so far.
    p.(q+r) = 4a + 26
    q.(p+r) = 2a + 24

    Can you tell me the next step of this? Thanks

    Answer: 2
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by r_maths View Post
    p = 2i + 3j + 4k
    q = i + 3j + 2k
    r = 2i + j + ak

    If p.(q+r) is 6 greater than q.(p+r) find the value of a.

    This is what I've done so far.
    p.(q+r) = 4a + 26
    q.(p+r) = 2a + 24

    Can you tell me the next step of this? Thanks

    Answer: 2
    i don't really like to work in the i-j-k notation, so let's write
    p = <2,3,4>
    q = <1,3,2>
    r = <2,1,a>

    i suppose your dot means the dot product

    Now, p.(q + r) = <2,3,4>.(<1,3,2> + <2,1,a>)
    ....................= <2,3,4>.<3,4,2+a>
    ....................= 6 + 12 + 8 + 4a
    ....................= 26 + 4a

    Now, q.(p + r) = <1,3,2>.(<2,3,4> + <2,1,a>)
    ....................= <1,3,2>.<4,4,4+a>
    ....................= 4 + 12 + 8 + 2a
    ....................= 24 + 2a

    Now we are told that p.(q+r) is 6 greater than q.(p+r), that is,

    q.(p + r) + 6 = p.(q + r)
    => 24 + 2a + 6 = 26 + 4a
    => 2a = 4
    => a = 2
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  3. #3
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    Thanks, i added 6 on to p.(q + r) instead of q.(p + r)
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by r_maths View Post
    Thanks, i added 6 on to p.(q + r) instead of q.(p + r)
    I actually made the same mistake , but i caught myself at the next line
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