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Dot product help

  1. Dec 18, 2014 #1
    1. The problem statement, all variables and given/known data
    If at some particular place and time the sun light is incident on the surface of the earth along
    a direction defined by the unitary vector – vˆ , where vˆ =(4, 3, 5)/sqrt (50) and with a power
    density P, what is the total power captured by a solar panel of 1.4 m2
    and with an efficiency
    of 12% which is oriented along the vector wˆ =(0, 1, 4) /sqrt(17) ?

    2. Relevant equations

    The dot/scalar product equation.
    3. The attempt at a solution
    I took the scalar product of -v and w, this gave me -23/sqrt(50*17), then multiply this by P*1.4*0.12, but my question is that the overall answer I get is negative due to the dot product. Is this possible as total power ? and am I doing this correctly ?.
     
  2. jcsd
  3. Dec 18, 2014 #2

    Doc Al

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    Staff: Mentor

    You want the component of sun light going into that panel, so you'd better use the dot product of ##-\hat{v}## and ##-\hat{w}##.
     
  4. Dec 19, 2014 #3
    Thank you for the reply.
    I think I am understanding what you are trying to say. So does it mean that -v points downwards going into the panel ? and it says the panel is orientated along w so I don't understand where does the into bit come from ? I taught if I take -w it would just mean now the panel is in the opposite direction. Unless orientated along w means the vector w is pointing upwards from the panel ?
     
  5. Dec 19, 2014 #4

    Doc Al

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    Staff: Mentor

    That's exactly what it means. The orientation of a plane is typically specified by a vector normal to the plane pointing out of the plane.
     
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