Solar Panels have to be installed carefully so that the tilt of the roof, and the direction to the sun, produce the largest possible electrical power in the solar panels.
A surveyor uses his instrument to determine the coordinates of the four corners of a roof where solar panels are to be mounted. In the picture , suppose the points are labelled counter clockwise from the roof corner nearest to the camera in units of meters P
(6, 8, 4) , P
(21, 8, 4), P
(21, 16, 10) and P
(6, 16, 10)
What are the components to the two edge vectors defined by A ⃗ = PV of P 2 – PV of P1 and B ⃗ = PV of P 4 – PV of P 1 ? (where PV stands for position vector)
Write the vector in standard notation with i ̂, j ̂ and k ̂ (where i ̂, j ̂ and k ̂ are the unit vectors along the three axes).
What are the magnitudes of the vectors A ⃗ and B ⃗ and in what units?
What are the components to the vector N ⃗ , perpendicular to A ⃗ and B ⃗ and the surface of the roof?
What is the magnitude of N ⃗ and its units? The sun is located along the unit vector S ⃗ = 1/2 i ̂-6/7 j ̂+1/7 k ̂. If the flow of solar energy is given by the vector F ⃗ = 910 S in units of watts/meter2 , what is the dot product of vectors F ⃗ 𝑤𝑖𝑡ℎ N ⃗ , and the units for this quantity?
What is the angle between vectors N ⃗ and S ⃗ ? What is the elevation angle of the sun above the plane of the roof? (cos 51° = 0.629 )