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Math Help - the component form of a vector + unit vector with same direction

  1. #1
    Newbie El Sparko's Avatar
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    the component form of a vector + unit vector with same direction

    i need to;

    write in component for the vector with the initial point P(6,2) and the final point Q(3,7)

    I think the answer is PQ = -3i +5j is that right?

    later in the question I have to write a unit vector with the same direction and I have no idea how to do this.

    Thanks for the help

    ES
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  2. #2
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    Quote Originally Posted by El Sparko View Post
    i need to;

    write in component for the vector with the initial point P(6,2) and the final point Q(3,7)

    I think the answer is PQ = -3i +5j is that right?
    Yes, that is correct.

    later in the question I have to write a unit vector with the same direction and I have no idea how to do this.

    Thanks for the help

    ES
    A unit vector has length 1. PQ is not a unit vector because its length is \sqrt{3^2+ 5^2}= \sqrt{9+ 25}= \sqrt{34}
    You can change the length of a vector while not changing the direction by multiplying or dividing both components by the same number. And you can change the length to 1 by dividing by \sqrt{34}.
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  3. #3
    Newbie El Sparko's Avatar
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    Quote Originally Posted by HallsofIvy View Post
    A unit vector has length 1. PQ is not a unit vector because its length is \sqrt{3^2+ 5^2}= \sqrt{9+ 25}= \sqrt{34}
    You can change the length of a vector while not changing the direction by multiplying or dividing both components by the same number. And you can change the length to 1 by dividing by \sqrt{34}.
    dividing what part by \sqrt{34} ?
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  4. #4
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    I said "dividing both components" of -3i+ 5j by \sqrt{3}.
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  5. #5
    Newbie El Sparko's Avatar
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    yes, sorry I misread your first post. thanks very much for your help.
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