Calculating Power of a Solar Panel

• eehelp
In summary, the question is asking for the total power captured by a solar panel with a surface area of 1.4 m2 and 12% efficiency, when it is oriented along the vector wˆ=(0, 1, 4)/sqrt(17) and receives sunlight with a power density P along the direction of the unit vector -vˆ=(4, 3, 5)/sqrt(50). The solution involves taking the dot product of -vˆ and -wˆ and multiplying it by P*1.4*0.12. The negative sign in front of the dot product represents the direction of the sunlight going into the panel, which is specified by the orientation of the panel along

Homework Statement

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) ?

Homework Equations

The dot/scalar product equation.

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 ?.

eehelp said:
which is oriented along the vector wˆ =(0, 1, 4) /sqrt(17) ?
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}##.