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Math Help - Vector help please.

  1. #1
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    Vector help please.

    Line 1 = -4i + j +3k + s(i + 5j - 2k)
    Line 2 = 3i - 7j + 9k + t(2i - 3j + k)

    The lines are skew.

    Question: Find the position vector of the point C on line 2 such that ∠ABC = 90.

    Annnd...i have no idea how...I've tried random things but nothing works.
    The answer is -7i + 8j + 4k

    Any help or prods in the right direction would be appreciated.
    Thank-you very much!
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  2. #2
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    Quote Originally Posted by AshleyT View Post
    Line 1 = -4i + j +3k + s(i + 5j - 2k)
    Line 2 = 3i - 7j + 9k + t(2i - 3j + k) The lines are skew.
    Question: Find the position vector of the point C on line 2 such that ∠ABC = 90.
    You have failed to tell us anything about A or B.
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  3. #3
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    Quote Originally Posted by Plato View Post
    You have failed to tell us anything about A or B.
    O, sorry!
    A and B have position vectors
    4i + 1j + 3k
    and
    3i + 6j + k
    respectively
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  4. #4
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    Quote Originally Posted by AshleyT View Post
    O, sorry!
    A and B have position vectors
    4i + 1j + 3k
    and
    3i + 6j + k
    respectively
    Then A and B are not on line 1 or line 2? And, in fact, line 1 has nothing to do with this problem? C, since it is on line 2, can be written with position vector (3+2t)i- (7+ 3t)j+ (9+ t)k.

    Then the vector from C to B is (3+2t- 3)i- (7+ 3t- 6)j+ (9+t- 1)k= 2ti- (1+ 3t)j+ (8+ t)k. The vector from A to B is (3- 4)i+ (6- 1)j+ (1- 3)k= -i+ 5j- 2k. The angle ABC will be 90 degrees if and only if those two vectors are orthogonal which itself is true if and only if their dot product is 0:
    -1(2t)- 5(1+ 3t)- 2(8+ t)= -25t- 21= 0 or t= -21/25. That does NOT give the C that you say is the answer. Are you sure you have copied everything correctly?
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  5. #5
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    Sorry, this is the entire question...i gave Line 1 because i thought it was needed.

    I'll attach the exam paper because i can't copy and paste very well from this laptop. Its question 7.

    Thankyou very much for your reply!
    Attached Files Attached Files
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  6. #6
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    So from the question paper it seems that you have copied the coordinates of both A and B incorrectly. That might account for not being able to get the answer right.
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  7. #7
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    Well it was more that i never even knew where to start lol!
    I kinda understand it now though, im going to try again tomorrow, vectors give me a headache!
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