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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
_{
1
}
(6, 8, 4) , P
_{
2
}
(21, 8, 4), P
_{
3
}
(21, 16, 10) and P
_{
4
}
(6, 16, 10)

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Question 1
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What are the components to the two edge vectors defined by AΒ β = PV of P
_{
2
}
β PV of P1 and BΒ β Β = PV of P
_{
4
}
β PV of P
_{
1
}
? (where PV stands for position vector)

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Question 2
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## Write the vector in standard notation with iΒ Μ, jΒ Μ Β and kΒ Μ (where iΒ Μ, jΒ ΜΒ and kΒ Μ are the unit vectors along the three axes).

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Question 3
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## What are the magnitudes of the vectors AΒ β and BΒ β and in what units?

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Question 4
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## What are the components to the vector NΒ β , perpendicular to AΒ β and BΒ β and the surface of the roof?

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Question 5
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What is the magnitude of NΒ β and its units? The sun is located along the unit vector SΒ β Β = 1/2 iΒ Μ-6/7Β jΒ Μ+1/7Β kΒ Μ. If the flow of solar energy is given by the vector FΒ βΒ = 910 S in units of watts/meter2 , what is the dot product of vectors FΒ β π€ππ‘β NΒ β , and the units for this quantity?

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Question 6
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## What is the angle between vectors NΒ β and SΒ β ? What is the elevation angle of the sun above the plane of the roof? (cos 51Β° = 0.629 )

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