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A vector perpendicular to a circle watch

    • Thread Starter

    Hello all,
    just came across a question that sort of confused me since I haven't really seen anything like it before. Anyway here it is.
    "Given that a = 2sinθi + ( 1-sinθ )j, find the value of the acute angle θ, so that a is perpendicular to the line x+y=1."
    I have tried a few approaches but none of the seem to work, its probably not too difficult once you get it, but would like some help if anyone has some time to spare.

    The given line can be written as y=1-x so a line perpendicular to this would have gradient (-1)/(-1)=1. Therefore, you want a to be parallel to the y=x line. For this to be the case, you would have 2sin=1-sinθ, which you can then solve for theta.
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Updated: January 15, 2010

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