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Math Help - Finding coordinate vector of point

  1. #1
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    Finding coordinate vector of point

    A point P in \mathbb{R}^n has coordinate vector \mathbf{p}. Find the coordinate vector of the point Q which is the reflection of P in the line l which passes through the point \mathbf{a} parallel to the direction \mathbf{d}
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  2. #2
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    Quote Originally Posted by acevipa View Post
    A point P in \mathbb{R}^n has coordinate vector \mathbf{p}. Find the coordinate vector of the point Q which is the reflection of P in the line l which passes through the point \mathbf{a} parallel to the direction \mathbf{d}
    I'm not certain if this will help:

    1. Draw a sketch.

    2. Since Q is the image of P by refelection about the line l the midpoint of \overline{PQ} belongs to the line l and the vector \vec d is perpendicular to \overrightarrow{PQ}. That means:

    \frac12(\vec p + \vec q)=\vec a + r \cdot \vec d
    and
    \vec d \cdot \overrightarrow{PQ} = 0

    3. Solve for \vec q.

    I've got:

    \vec q = 2\vec a + 2r \cdot \vec d - \vec p
    Attached Thumbnails Attached Thumbnails Finding coordinate vector of point-pktspieglangerade.png  
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  3. #3
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    Quote Originally Posted by earboth View Post
    I'm not certain if this will help:

    1. Draw a sketch.

    2. Since Q is the image of P by refelection about the line l the midpoint of \overline{PQ} belongs to the line l and the vector \vec d is perpendicular to \overrightarrow{PQ}. That means:

    \frac12(\vec p + \vec q)=\vec a + r \cdot \vec d
    and
    \vec d \cdot \overrightarrow{PQ} = 0

    3. Solve for \vec q.

    I've got:

    \vec q = 2\vec a + 2r \cdot \vec d - \vec p
    Thank you so much. That was really helpful
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