# Dot product help

## 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 ?.

Doc Al
Mentor
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}##.

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 ?

Doc Al
Mentor
Unless orientated along w means the vector w is pointing upwards from the panel ?
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.